Answer:
c = 5
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 = -¹/₃
- Point = (-1, 0)
Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx + b\\\implies 0 & = -\dfrac{1}{3}(-1)+b\\0 & = \dfrac{1}{3}+b\\-\dfrac{1}{3}&=b\\ \implies b&=-\dfrac{1}{3}\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{1}{3}x-\dfrac{1}{3}}[/tex]
Substitute the point (c, -2) into the equation and solve for c:
[tex]\begin{aligned} y&=-\dfrac{1}{3}x-\dfrac{1}{3}\\\implies -2&=-\dfrac{1}{3}c-\dfrac{1}{3}\\-2+\dfrac{1}{3}&=-\dfrac{1}{3}c-\dfrac{1}{3}+\dfrac{1}{3}\\-\dfrac{5}{3}&=-\dfrac{1}{3}c\\-\dfrac{5}{3} \cdot 3&=-\dfrac{1}{3}c \cdot 3\\-5&=-c\\\implies c & = 5\end{aligned}[/tex]
Solution
Therefore, the value of c is 5.
