We can use information presented in a graph to write an equation in slope-intercept form.

Writing an equation from a graph - Examples

Example 1 :

A video club charges a one-time membership fee plus a rental fee for each DVD borrowed. Use the graph to write an equation in slope-intercept form to represent the amount spent, y, on x DVD rentals.

Solution :

Step 1 :

Choose two points on the graph, (x₁, y₁) and (x₂, y₂), to find the slope.

Find the ratio between change in y-values and change in x-

m = (y₂ - y₁) / (x₂ - x₁)

Substitute (0, 8) for (x₁, y₁) and (8, 18) for (x₂, y₂).

m = (18 - 8) / (8 - 0)

m = 10 / 8

m = 1.25

Step 2 :

Read the y-intercept from the graph. That is, the point at which the line cuts y-axis.

The y-intercept is 8.

b = 8

Step 3 :

Let us use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.

y = mx + b (Slope-intercept form)

Plug m = 1.25 and b = 8.

y = 1.25x + 8

Example 2 :

The cash register subtracts $2.50 from a $25 Coffee Café gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation.

Solution :

Step 1 :

Choose two points on the graph, (x₁, y₁) and (x₂, y₂), to find the slope.

Find the ratio between change in y-values and change in x-

m = (y₂ - y₁) / (x₂ - x₁)

Substitute (0, 25) for (x₁, y₁) and (10, 0) for (x₂, y₂).

m = (0 - 25) / (10 - 0)

m = -25 / 10

m = -2.5

Step 2 :

Read the y-intercept from the graph. That is, the point at which the line cuts y-axis.

The y-intercept is 25.

Step 3 :

Let us use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.

y = -2.5x + 25 (Slope-intercept form)

Plug m = -2.5 and b = 25.

y = -2.5x + 25

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