Answer:
[tex]y = \frac{1}{2} x - 3[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Using the gradient formula above,
gradient of line
[tex] = \frac{ - 1 - ( - 7)}{4 - ( - 8)} [/tex]
[tex] = \frac{ - 1 + 7}{4 + 8} [/tex]
[tex] = \frac{6}{12} [/tex]
[tex] = \frac{1}{2} [/tex]
Substitute m= ½ into the equation:
y= ½x +c
To find the value of c, substitute a pair of coordinates.
When x= 4, y= -1,
[tex] - 1 = \frac{1}{2} (4) + c[/tex]
-1= 2 +c
c= -1 -2 (-2 on both sides)
c= -3
∴ The equation of the line is y= ½x -3.
