y = -x + 7 is the slope intercept form of (9, -2) and (4, 3)
Given two points are (9, -2) and (4, 3)
We have to find the slope intercept form
The slope intercept form is given as:
y = mx + c -------- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Let us first find the slope of line
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text {Here } x_{1}=9 ; y_{1}=-2 ; x_{2}=4 ; y_{2}=3[/tex]
[tex]m=\frac{3-(-2)}{4-9}=\frac{5}{-5}=-1[/tex]
Thus slope of line is m = -1
To find the y - intercept:
Substitute m = -1 and (x, y ) = (9, -2) in eqn 1
-2 = -1(9) + c
-2 = -9 + c
c = -2 + 9
c = 7
Substitute m = -1 and c = 7 in eqn 1
y = -1x + 7
y = -x + 7
Thus the required slope intercept form is found
