Problem 83

Question

If one point on a line is \((3,-1)\) and the line's slope is \(-2,\) find the \(y\) -intercept.

Step-by-Step Solution

Verified
Answer
The y-intercept is 5.
1Step 1: Understand the slope-intercept form
The equation of a line can be written in the form \(y = mx + c\), where m is the slope and c is the y-intercept.
2Step 2: Substitute the given point and slope into the equation
Substituting the given point \((3,-1)\) and the slope \(-2\) into our equation gives us \(-1 = -2(3) + c\). This equation then simplifies to \(-1 = -6 + c\).
3Step 3: Solve for the y-intercept
Solving for c by rearranging the equation \(-1 = -6 + c\), we get \(c = -1 + 6\). Solving that, we get \(c = 5\).