Question

How do you write an equation for the line that has a x-intercept of -5 and a y-intercept of 2?

Answer 1

`y=2/5x+2`

Explanation:

Equation of a line in slope-intercept form: y=mx+b, m represents slope, b represents y-intercept

x-intercept: (-5, 0)

y-intercept: (0, 2)

Our current equation is: y=mx+2

To find the slope using two points, divide the difference of the y-coordinates by the difference of the x-coordinates

`(y_2-y_1)/(x_2-x_1)`

`(2-0)/(0-(-5)) rarr` Plug the points in

`2/5 rarr` This is the slope

The equation (in slope-intercept form) is `y=2/5x+2`

Answer 2

Find the slope of the line and then substitute to put the equation into a standard form such as the y intercept form.

Explanation:

To find the slope find the ratio of the increase of y to x

slope =`(y_1-y_2)/(x_1-x_2)`

the y intercept is ( 0,2)
The x intercept is ( -5,0)

putting these into the slope equation. gives

slope = `( 2-0)/{0 -(-5)}` This equals

slope = `2/5`

The slope is m in the y intercept form so

`y = 2/5 x + b`. Substitue values for x and y and solve for b.

`2 = 2/5 ( 0) + b` This gives

`2 = b` put to 2 for b

`y = 2/5x + 2`