Question

How do you write an equation of a line that passes through the point (-8, -5) and has a slope of -5/4?

Answer 1

`y=-5/4x-15`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`"here " m=-5/4" and " (x_1,y_1)=(-8,-5)`

substituting these values into the equation.

`y-(-5)=-5/4(x-(-8))`

`rArry+5=-5/4(x+8)larr" in point-slope form"`

distributing and simplifying gives the equation in an alternative form.

`y+5=-5/4x-10`

`rArry=-5/4x-15larr" in slope-intercept form"`