Question

Write an equation in slope intercept form for the line that passes thru the points (4,-2) and (-5,7)

Answer 1

Answer:

y = -x + 2

Step-by-step explanation:

The equation of a line in a slope intercept form is given as :

$y = mx + c$, where m is the gradient and c, y - intercept.

First, let us find the gradient, m of the line that passes through the points, (4,-2) and (-5,7) using the relation ;

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

By substitution we get

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

$\implies m = \frac{7 + 2}{ - (5 + 4)}$

$\implies m = \frac{9}{ - 9} = - 1$

We substitute any of the points and the value of m into y= mx + c to find the value for c.

$\implies - 2 = 4( - 1) + c$

$\implies - 2 = - 4+ c$

Adding 4 to both sides.

$\implies 4- 2= - 4 + 4+ c$

$\implies 4- 2= + c$

$\implies c = 2$

Hence the equation of the line is :

y = -x +2