Question

A line has a slope of 6/5 and includes the points (-2, -3) and (r, 3). What is the value of r?​

Answer 1

r = 3

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 = ⁶/₅
• Point = (-2, -3)

Substitute the given slope and point into the formula and solve for b:

`\begin{aligned}y & = mx+b\\\implies -3 & = (6)/(5)(-2)+b\\-3 & = -(12)/(5)+b\\-3 +(12)/(5) & = b\\\implies b & = -(3)/(5)\end{aligned}`

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

`\boxed{y=(6)/(5)x-(3)/(5)}`

Substitute the point (r, 3) into the equation and solve for r:

`\begin{aligned}y & = (6)/(5)x-(3)/(5)\\\implies 3 & = (6)/(5)r-(3)/(5)\\5 \cdot 3& = 5 \cdot \left((6)/(5)r-(3)/(5)\right)\\15 & = 6r-3\\15+3&=6r-3+3\\ 18 & = 6r\\(18)/(6) & = (6r)/(6)\\3 & = r\\ \implies r & =3\end{aligned}`

Solution

Therefore, the value of r is 3.