An equation in point slope form of the line that passes thru (4,-5); m=6​

y = -x + 2

Step-by-step explanation:

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

y = mx + cy=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}m=

x

2

−x

1

y

2

−y

1

By substitution we get

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

−5−4

7−(−2)

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

−(5+4)

7+2

\implies m = \frac{9}{ - 9} = - 1⟹m=

−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⟹−2=4(−1)+c

\implies - 2 = - 4+ c⟹−2=−4+c

Adding 4 to both sides.

\implies 4- 2= - 4 + 4+ c⟹4−2=−4+4+c

\implies 4- 2= + c⟹4−2=+c

\implies c = 2⟹c=2

Hence the equation of the line is :

y = -x +2