How to Find Slope? (+FREE Worksheet!)

How to Find Slope? (+FREE Worksheet!)
Algebra 1

How to Find the Slope of a Line

Slope is one number that tells you how steep a line is and which way it tilts. Master it and you unlock graphing lines, writing equations in \(y=mx+b\), and every linear word problem you’ll meet. We’ll find slope from two points, from an equation, and straight off a graph — with a solver, drills, and a worksheet maker a tap away.

Tutor-style math help

Find Slope: what to notice and how to work it

Linear skill
Linear topics are about constant rate of change. The slope tells how fast y changes for each 1-unit change in x, and an intercept anchors the line on an axis.

What to notice first

Slope is the rate of change: vertical change divided by horizontal change. Read it as rise over run, not as two unrelated subtractions.

Common student mistake

Do not mix up x-intercepts and y-intercepts. At an x-intercept, y = 0; at a y-intercept, x = 0.

Key formulas and cues

\(m=\frac{y_2-y_1}{x_2-x_1}\)
\(y=mx+b\)
\(y-y_1=m(x-x_1)\)
\(Ax+By=C\)
runrise yx

A reliable path

  1. Find slopeUse two points, a table, or the coefficient of x in slope-intercept form.
  2. Find an anchorUse a point or intercept so the line is in the right location.
  3. Check directionPositive slope rises left to right; negative slope falls left to right.

Worked examples

Find slope from two points

Example: \((1,4)\) and \((3,10)\)
  1. Change in y is 10 – 4 = 6.
  2. Change in x is 3 – 1 = 2.
  3. Divide rise by run.
Answer: \(m=3\)

Write slope-intercept form

Example: slope 3 and y-intercept -2
  1. Use y = mx + b.
  2. Put m = 3 and b = -2.
  3. Write the line.
Answer: \(y=3x-2\)
Open pop-up practice
Try one before moving on
Try: Find the slope through \((0,2)\) and \((4,10)\).
Answer: \(m=2\).
Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.
⚡ Step-by-Step Solver📄 Worksheet Maker✏️ Practice Drills📇 Flashcards
Illustration of students learning How to Find the Slope of a Line

Picture walking up a hill. A gentle rise is easy; a steep one makes your legs burn. Slope is the math version of that feeling — a single number that captures how fast a line climbs or falls as you move to the right. Get comfortable with it and you’ll breeze through graphing lines, writing equations in \(y=mx+b\), and every linear word problem that comes your way. Let’s build it up slowly, one idea at a time.

The big idea

What Is Slope?

Slope measures the tilt of a line as the ratio of how much it goes up or down to how much it goes across — we say rise over run. For any two points \((x_1, y_1)\) and \((x_2, y_2)\) on the line, the slope \(m\) is:

\(m = \dfrac{\text{rise}}{\text{run}} = \dfrac{y_2 – y_1}{x_2 – x_1}\)

How to find slope from two points (3 steps):

  1. Subtract the \(y\)-values for the rise.
  2. Subtract the \(x\)-values, in the same order, for the run.
  3. Divide and simplify — that’s your slope.

The sign tells you the direction and the size tells you the steepness. As a feel for the numbers: a slope of \(1\) is a 45° line, a slope of \(2\) is twice as steep, and a slope of \(\tfrac12\) is gentle.

Positive slopeLine rises as you move right.
Negative slopeLine falls as you move right.
Zero slopePerfectly flat (horizontal line).
Undefined slopeStraight up and down (vertical line).

Slope Comes in Three Disguises: Points, Equations, and Graphs

Slope shows up in three disguises — as two points, as an equation, and as a picture. Here’s how to handle each, and we’ll work all three below so you actually see them in action.

From two points

Use the formula

When you’re handed two coordinate pairs.

  1. Label them \((x_1,y_1)\) and \((x_2,y_2)\).
  2. Subtract the \(y\)’s for the rise.
  3. Subtract the \(x\)’s (same order!) for the run.
  4. Divide and simplify.
\((1,3)\) and \((4,9)\):
\(m=\dfrac{9-3}{4-1}=\dfrac{6}{3}=\) 2
From an equation

Read off \(m\)

When the line is in slope-intercept form.

  1. Get the equation into \(y = mx + b\).
  2. The number multiplying \(x\) is the slope.
  3. The lone number \(b\) is the \(y\)-intercept.
In \(y = 3x + 6\), the slope is 3.
From a graph

Count rise over run

When you can see the line.

  1. Pick two points the line clearly crosses.
  2. Count up or down for the rise (up is +, down is −).
  3. Count across for the run (right is +, left is −).
  4. Write rise ÷ run.
The line below rises 4 and runs 2, so \(m=\tfrac{4}{2}=\) 2.
Tutor tip: The number-one slip is subtracting the \(x\)’s and \(y\)’s in a different order. Whatever point you call “first,” use it first on the top and the bottom — then the sign takes care of itself.
See it graphically

Rise over run, right on the grid

This is the line through \((1,1)\) and \((3,5)\) — the same points as Exercise 1 below. Going from the first point to the second, the line climbs up 4 (rise) and moves right 2 (run), so \(m=\tfrac{4}{2}=2\). Drop any two points into the solver to see the slope and the line appear.

⚡ Find a slope
y = 2x − 1(3, 5)

Worked Examples

Read each one slowly and try to call out the next step before you see it. Each line is drawn so you can see the rise and run.

Example A — From two points

Find the slope through \((1,3)\) and \((4,9)\).

  1. Rise = difference of \(y\): \(9 – 3 = 6\).
  2. Run = difference of \(x\), same order: \(4 – 1 = 3\).
  3. Divide: \(m = \dfrac{6}{3} = 2\) — up 2 for every step right.

Answer: \(m = 2\)

m = 2(4, 9)

Example B — Negatives & a fraction

Find the slope through \((4,-6)\) and \((-3,-8)\).

  1. Rise: \(-8 – (-6) = -2\).
  2. Run, same order: \(-3 – 4 = -7\).
  3. Divide: \(m = \dfrac{-2}{-7} = \dfrac{2}{7}\). A clean fraction is the answer — don’t force a decimal.

Answer: \(m = \tfrac{2}{7}\)

m = 2/7(4, -6)

Example C — From an equation

Find the slope of \(y = 3x + 6\).

  1. The equation is already in \(y = mx + b\) form.
  2. The slope is the coefficient of \(x\): \(m = 3\).
  3. The lone number, \(6\), is the \(y\)-intercept — the line crosses at \((0,6)\).

Answer: \(m = 3\)

y = 3x + 6(0, 6)

Example D — From a graph

Use the line through \((1,1)\) and \((3,5)\).

  1. Pick the two marked points.
  2. Count from the first: up 4 (rise), right 2 (run).
  3. Divide: \(m = \dfrac{4}{2} = 2\).

Answer: \(m = 2\)

m = 2(3, 5)

Example E — A vertical line (undefined)

Find the slope through \((4,1)\) and \((4,7)\).

  1. Rise: \(7 – 1 = 6\).
  2. Run: \(4 – 4 = 0\).
  3. \(m = \dfrac{6}{0}\) — division by zero, so the slope is undefined. Every vertical line is like this.

Answer: undefined

x = 4(4, 7)

Example F — A horizontal line (zero)

Find the slope through \((19,3)\) and \((20,3)\) — the same flatness as the line drawn at \(y=3\).

  1. Rise: \(3 – 3 = 0\).
  2. Run: \(20 – 19 = 1\).
  3. \(m = \dfrac{0}{1} = 0\). Matching \(y\)-values always mean a flat line, slope zero.

Answer: \(m = 0\)

y = 3(1, 3)

Example G — From a table

A table lists \(x = 1, 3\) with outputs \(y = 4, 10\). Find the slope.

  1. Read two rows as points: \((1,4)\) and \((3,10)\).
  2. Apply the formula: \(m = \dfrac{10 – 4}{3 – 1} = \dfrac{6}{2}\).
  3. Simplify: \(m = 3\). On a true line, any two rows give the same slope.

Answer: \(m = 3\)

m = 3(3, 10)

Slope in the Wild

Slope isn’t just a classroom number — it’s the rate at which one thing changes against another. A car holding a steady 60 mph traces a distance-vs-time line with slope \(60\) (miles over hours). A wheelchair ramp that rises 4 inches over 12 inches of length has slope \(m=\tfrac{\text{rise}}{\text{run}}=\tfrac{4}{12}=\tfrac13\). A roof’s “pitch,” a hill’s grade, the cost per extra topping on a pizza — anywhere a quantity changes steadily, slope is the number measuring how fast.

Slip-Ups That Cost Easy Points

  • Mixing up the order. If \((4,-6)\) is your first point, it stays first on top and bottom: \(\frac{-8-(-6)}{-3-4}\), never \(\frac{-8-(-6)}{4-(-3)}\). Pick an order and commit.
  • Putting run over rise. Slope is rise over run — the \(y\)-difference goes on top. Flipping it is a classic.
  • Subtracting negatives carelessly. Subtracting a negative adds: \(9-(-3)=12\). Write the double sign out so you don’t drop it.
  • Confusing zero and undefined. A horizontal line has slope \(0\); a vertical line is undefined (division by zero). Flat is zero; straight up is undefined.

Your Turn: Find These Slopes

Work each one by hand, then reveal the answers. If one feels shaky, the step-by-step solver will walk you through it.

  1. \((1, 1)\) and \((3, 5)\)
  2. \((4, -6)\) and \((-3, -8)\)
  3. \((7, -12)\) and \((5, 10)\)
  4. \((19, 3)\) and \((20, 3)\)
  5. \((15, 8)\) and \((-17, 9)\)
  6. \((6, -12)\) and \((15, -3)\)
Show answers
  1. \(\color{blue}{2}\)
  2. \(\color{blue}{\frac{2}{7}}\)
  3. \(\color{blue}{-11}\)
  4. \(\color{blue}{0}\)
  5. \(\color{blue}{-\frac{1}{32}}\)
  6. \(\color{blue}{1}\)
Keep practicing

Make Your Own Slope Worksheet

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Frequently Asked Questions

What does slope actually represent?

It’s the rate of change of a line — how much \(y\) changes for every step \(x\) takes to the right. A slope of 2 means “up 2 for every 1 across.” In real life it’s things like speed, price per item, or how steep a ramp is.

Does it matter which point I call “first”?

No — as long as you’re consistent. Whichever point you use first in the top subtraction, use first in the bottom too. You’ll land on the same slope either way.

What’s the difference between zero slope and undefined slope?

A horizontal line has slope \(0\) (no rise). A vertical line has an undefined slope, because the run is \(0\) and you can’t divide by zero. “Flat” is zero; “straight up” is undefined.

How do I find slope from an equation that isn’t solved for \(y\)?

Rearrange it into \(y = mx + b\) first. Once \(y\) is alone on the left, the number in front of \(x\) is your slope.

How do I find slope from a table?

Pick any two rows as your two points and use the same formula: the change in the output (\(y\)) over the change in the input (\(x\)). If the table is linear, every pair of rows gives the same slope — a quick way to check it’s really a line.

Related Topics

Graphing Lines Writing Linear Equations Finding Midpoint Distance Between Points Systems of Equations ← Algebra 1 Hub

Continue Your Study

Ready for the next step? Pick up right where this lesson leaves off:

Up nextWriting Linear EquationsContinue with Linear FunctionsOpen lesson →Up nextHow to Graph Linear InequalitiesContinue with Linear FunctionsOpen lesson →Up nextFinding the x-InterceptContinue with Linear FunctionsOpen lesson →
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