Question

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

Answer 1

Answer:

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

Step-by-step 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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

Calculate the slope:

$m=\dfrac{4-(-5)}{-5-(-7)}=\dfrac{9}{2}$

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

$y-4=\dfrac{9}{2}(x-(-5))$

$y-4=\dfrac{9}{2}(x+5)$ → the point-slope form

Convert to the standard form Ax + By = C :

$y-4=\dfrac{9}{2}(x+5)$         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