Answer:
r = -6
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Slope 3/4
This means that [tex]m = \frac{3}{4}[/tex], and thus:
[tex]y = \frac{3}{4}x + b[/tex]
(6,3)
This means that when [tex]x = 6, y = 3[/tex]. We use this to find b. So
[tex]y = \frac{3}{4}x + b[/tex]
[tex]3 = \frac{3}{4}(6) + b[/tex]
[tex]b = 3 - \frac{18}{4} = \frac{12}{4} - \frac{18}{4} = -\frac{6}{4}[/tex]
So
[tex]y = \frac{3}{4}x - \frac{6}{4} = \frac{3x - 6}{4}[/tex]
(-6, r)
r is y when [tex]x = -6[/tex]. So
[tex]y = \frac{3(-6) - 6}{4} = -6[/tex]
So r = -6.
