Question

Find the equation for the linear function that passes through the points (−5,−4) and (5,2). Answers must use whole numbers and/or fractions, not decimals.

Use the line tool below to plot the two points.


State the slope between the points as a reduced fraction.

State the y-intercept of the linear function.

State the linear function

Answer 1

The equation of the line is y = 0.6*x - 1, the graph is in the image at the end.

How to find the linear equation?

A linear equation in the slope-intercept form can be written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points (−5,−4) and (5,2), so the slope is:

a = (2 + 4)/(5 + 5) = 6/10 = 0.6

y = 0.6*x + b

And it passes through (5, 2), then:

2 = 0.6*5 + b

2 - 0.6*5 = b

-1 = b

The equation is:

y = 0.6*x - 1

The graph is in the image below.

Answer 2

`y = (3)/(5) x - 1`

Explanation:

1) find m or the slope:

`m = ( - 4 - 2)/( - 5 - 5) = (3)/(5)`

2) plug in coordinate pair to solve for b:

`y = (3)/(5) x - b`

`2 = (3)/(5) (5) + b`

`b = - 1`

3) now you have m and b so you have your formula