Answer:
r = 3
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\large\boxed{y=mx+b}[/tex]
where:
- m is the slope.
- b is the y-intercept.
Given:
- Slope = ⁶/₅
- Point = (-2, -3)
Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx+b\\\implies -3 & = \dfrac{6}{5}(-2)+b\\-3 & = -\dfrac{12}{5}+b\\-3 +\dfrac{12}{5} & = b\\\implies b & = -\dfrac{3}{5}\end{aligned}[/tex]
Substitute the given slope and found value of b into the formula to create an equation for the line:
[tex]\boxed{y=\dfrac{6}{5}x-\dfrac{3}{5}}[/tex]
Substitute the point (r, 3) into the equation and solve for r:
[tex]\begin{aligned}y & = \dfrac{6}{5}x-\dfrac{3}{5}\\\implies 3 & = \dfrac{6}{5}r-\dfrac{3}{5}\\5 \cdot 3& = 5 \cdot \left(\dfrac{6}{5}r-\dfrac{3}{5}\right)\\15 & = 6r-3\\15+3&=6r-3+3\\ 18 & = 6r\\\dfrac{18}{6} & = \dfrac{6r}{6}\\3 & = r\\ \implies r & =3\end{aligned}[/tex]
Solution
Therefore, the value of r is 3.
