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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