To find the value of r
We will follow the steps below
Usinf the equation of a slope:
slope(m) =
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]from the question given;
m= -3/4
x₁ = 3
y₁=4
x₂=-1
y₂=r
substituting the values into the slope formula
[tex]\frac{-3}{4}\text{ = }\frac{r-4}{-1-3}[/tex]we can now simplify and then solve for r
[tex]\frac{-3}{4}\text{ = }\frac{r-4}{-4}[/tex]
cross-multiply
-3 x -4 = 4(r-4)
12 = 4(r-4)
Divide both-side of the equation by 4
[tex]\frac{12}{4}\text{ = }\frac{4(r-4)}{4}[/tex]3 = r - 4
add 4 to both-side of the equation
3+4 = r-4+4
7 = r
r=7
Therefore the value of r is 7
