WRITING LINEAR EQUATIONS FROM A GRAPH

Write the slope-intercept form of the equation of each line.

Problem 1 :

Solution:

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-values.

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

The y-intercept is 0.

b = 0

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

y = mx + b (slope intercept form)

Substitute m = 3 and b = 0

y = 3x + 0

y = 3x

Problem 2 :

Solution:

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-values.

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

The y-intercept is 1.

b = 1

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

y = mx + b (slope intercept form)

Substitute m = -3/5 and b = 1

y = -(3/5)x + 1

Problem 3 :

Solution:

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-values.

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

The y-intercept is -4.

b = -4

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

y = mx + b (slope intercept form)

Substitute m = -2/3 and b = -4

Problem 4 :

Solution:

y is constant.

y = b

b = 4 

So, y = 4

Problem 5 :

Solution:

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-values.

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

The y-intercept is 5.

b = 5

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

y = mx + b (slope intercept form)

Substitute m = 1 and b = 5

y = x + 5

Problem 6:

Solution:

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-values.

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

The y-intercept is 0.

b = 0

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

y = mx + b (slope intercept form)

Substitute m = 5/2 and b = 0

y = 5/2x + 0

y = (5/2)x

Problem 7 :

Solution:

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-values.

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

The y-intercept is 5.

b = 5

Substitute m = 7/2 and b = 5

Problem 8 :

Solution:

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-values.

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

The y-intercept is 4.

b = 4