Answer:
The answer to your question is y = -5/4x + 9/4
Step-by-step explanation:
Data
A (5, -4)
B (-3, 6)
Formula
Slope m = (y2 - y1) / (x2 - x1)
x1 = 5 y1 = -4
x2 = -3 y2 = 6
-Substitution
m = (6 + 4) / (-3 - 5)
-Simplification
m = 10/-8
m = -5/4
-Find the equation of the line
y - y1 = m(x - x1)
y + 4 = -5/4(x - 5)
y + 4 = -5/4x + 25/4
-Solve for y
y = -5/4x + 25/4 - 4
y = -5/4x + 9/4
y = -5/4x + 2.25
gradient -
[tex] = \frac{y - y1}{x - x1} \\ = \frac{ - 4 - 6}{5 + 3} \\ = \frac{ - 5}{4} [/tex]
equation of the line -
[tex](y - y1) = m(x - x1) \\ (y + 4) = \frac{ - 5}{4} (x - 5) \\ (y + 4) = \frac{ - 5}{4} x - 6.2 \\ y = \frac{ - 5}{4} x + 2.25[/tex]
