How to Write a Point-slope Form Equation from a Graph?

Step 1: Identify a point on the line

Step 2: Find the slope of the line

Step 3: Write the equation using the point-slope form

Writing a Point-slope Form Equation from a Graph, Examples 1

Solution:

The graph shows that the line passes through point \((0, 2)\). Therefore, \((x_1, y_1) = (0, 2)\). Consider another random point on the line such as \(-2,-1)\)

Step 2: Find the slope of the line

Using the two points \((0, 2)\) and \((-2, -1)\), you can find the slope of the line as follows:

\(m = \frac{(y_2 – y_1)}{(x_2 – x_1)}\)

\(m = \frac{(2+1)}{(0+2)}\)

\(m = \frac{3}{2}\)

Therefore, the slope of the line is \(\frac{3}{2}\).

Step 3: Write the equation using the point-slope form

Now that you have the slope and a point on the line, you can write the equation of the line in the point-slope form:

\(y – y_1 = m(x – x_1)\)
\(y +1 = \frac{3}{2}(x +2)\)

This is the equation of the line in point-slope form.

Exercises for Writing a Point-slope Form Equation from a Graph

Write the equation of the line in point-slope form.

1.

2.

1. \(\color{blue}{y\:+\:2\:=−2\left(x\:−\:1\right)}\)
2. \(\color{blue}{y\:-\:3\:=\left(-\frac{1}{2}\right)\left(x+1\right)}\)

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Frequently Asked Questions

How do you write an equation in point-slope form from a graph?

Pick one point where the line crosses grid lines exactly and call it (x₁, y₁). Use a second clear point to count rise over run for the slope m. Then substitute into y − y₁ = m(x − x₁). If a line passes through (1, 3) and (3, 7), the slope is 4 ÷ 2 = 2, so one answer is y − 3 = 2(x − 1).

How do you write an equation in point-slope form?

You need one point on the line and the slope. Put them into y − y₁ = m(x − x₁), keeping the minus signs in the formula. For slope −3 through the point (−2, 4), you get y − 4 = −3(x − (−2)), which simplifies to y − 4 = −3(x + 2). A negative coordinate turns the minus sign into a plus, which is where many sign mistakes happen.

What is point-slope form used for?

Point-slope form lets you write a line’s equation quickly when you know a point and the slope but not the y-intercept. It is ideal for graphs where the line crosses the y-axis at a fraction that is hard to read. From y − 1 = ½(x − 4) you can still find the intercept by distributing: y = ½x − 2 + 1, so y = ½x − 1.

How do you write point-slope form equations from two points?

First find the slope with m = (y₂ − y₁) ÷ (x₂ − x₁), then use either point in y − y₁ = m(x − x₁). For (2, −1) and (6, 7), m = (7 − (−1)) ÷ (6 − 2) = 8 ÷ 4 = 2. Using (2, −1) gives y + 1 = 2(x − 2); using (6, 7) gives y − 7 = 2(x − 6). Both describe the same line.

Related Lessons You May Like

• How to find the slope of a line
• How to write linear equations from y-intercept and slope
• How to graph linear equations
• Parallel and perpendicular lines
• How to solve systems of equations

For a workbook on slope, linear equations, and the slope-intercept form, Algebra I for Beginners walks the material from first principles. Pre-Algebra for Beginners covers the prerequisites.