Question

What is the equation of a line that has an x-intercept of -2 and a y-intercept of -5?

Answer 1

`y=-5/2x-5`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"here "b=-5`

`y=mx-5larrcolor(blue)"is the partial equation"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-2,0)" and "(x_2,y_2)=(0,-5)`

`m=(-5-0)/(0-(-2))=(-5)/2=-5/2`

`y=-5/2x-5larrcolor(red)" is the equation of the line"`

Answer 2

`y=-5/2x - 4`

Explanation:

You have 2 points on the line:

`(-2,0), (0-5)`

Use slope point formula

First you determine the slope:

`(color(blue)(x_1),color(blue)(y_1)) = (-2,0)`

`(color(red)(x_2),color(red)(y_2))=(0,-5)`

`color(green)m =(color(red)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(blue)(x_1))`

`color(green)m =(color(red)(-5)-color(blue)(0))/(color(red)(0)-color(blue)((-2)))=-5/2`

Now use the Point Slope form of a line:

`(y-color(blue)(y_1)) = color(green)m(x-color(blue)(x_1))`

`(y-color(blue)((-5))) = color(green)(-5/2)(x-color(blue)(0))`

`y+5=-5/2x`

`y=-5/2x - 5`

graph{y=-5/2x - 5 [-10, 10, -5, 5]}