Question

A line that includes the points (c, -2) and (-1, 0) has a slope of -1/3 What is the value of c?​

Answer 1

c = 5

Explanation:

Slope-intercept form of a linear equation:

`\large\boxed{y=mx+b}`

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:

`\begin{aligned}y & = mx + b\\\implies 0 & = -(1)/(3)(-1)+b\\0 & = (1)/(3)+b\\-(1)/(3)&=b\\ \implies b&=-(1)/(3)\end{aligned}`

Substitute the given slope and found value of b into the formula to create an equation for the line:

`\boxed{y=-(1)/(3)x-(1)/(3)}`

Substitute the point (c, -2) into the equation and solve for c:

`\begin{aligned} y&=-(1)/(3)x-(1)/(3)\\\implies -2&=-(1)/(3)c-(1)/(3)\\-2+(1)/(3)&=-(1)/(3)c-(1)/(3)+(1)/(3)\\-(5)/(3)&=-(1)/(3)c\\-(5)/(3) \cdot 3&=-(1)/(3)c \cdot 3\\-5&=-c\\\implies c & = 5\end{aligned}`

Solution

Therefore, the value of c is 5.