Answer:
[tex]y = \frac{13}{4}x -21[/tex]
Step-by-step explanation:
Given points (4, -8) and (8, 5):
Let (x1, y1) = (4, -8)
(x2, y2) = (8, 5)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
[tex]m = \frac{5 - (-8)}{8 - 4} = \frac{5 + 8}{8 - 4} = \frac{13}{4}[/tex]
Therefore, the slope of the equation is 13/4.
Next, to find the y-intercept, use one of the given points (4, -8) and the slope. Substitute these values into the slope-intercept form to solve for the y-intercept, b:
y = mx + b
[tex]-8 = \frac{13}{4}(4) + b[/tex]
-8 = 13 + b
Subtract 13 from both sides:
-8 - 13 = 13 - 13 + b
-21 = b
Therefore, given the slope, [tex]m = \frac{13}{4}[/tex] , and the y-intercept, b = -21:
The linear equation in slope-intercept form is: [tex]y = \frac{13}{4}x -21[/tex]
