Question

A line passes through (–7, –5) and (–5, 4).Write an equation for the line in point-slope form.

Rewrite the equation in standard form using integers.

Answer 1

`\large\boxed{y-4=(9)/(2)(x+5)}\\\boxed{9x-2y=-53}`

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

m - slope

The formula of a slope:

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

We have the points (-7, -5) and (-5, 4).

Calculate the slope:

`m=(4-(-5))/(-5-(-7))=(9)/(2)`

Put it and coordinates of the point (-5, 4) to the equation:

`y-4=(9)/(2)(x-(-5))`

`y-4=(9)/(2)(x+5)` → the point-slope form

Convert to the standard form Ax + By = C :

`y-4=(9)/(2)(x+5)` multiply both sides by 2

`2y-8=9(x+5)` use the distributive property

`2y-8=9x+45` add 8 to both sides

`2y=9x+53` subtract 9x from both sides

`-9x+2y=53` change the signs

`9x-2y=-53` → the standard form