Problem 84 - College Algebra Essentials

Question

If one point on a line is \((2,-6)\) and the line's slope is \(-\frac{3}{2},\) find the \(y\) -intercept.

Step-by-Step Solution

Answer

The y-intercept of the line is -3.

Step 1: Write down the equation of a line

The slope-intercept form of the line is given by \(y = mx + b\). Here, \(m\) and \(b\) are the slope and y-intercept of the line respectively.

Step 2: Substitute the given values into the equation

We are given a point, which is \((2, -6)\) and the slope of the line which is \(-\frac{3}{2}\). We substitute these into the line equation and we get \(-6 = -\frac{3}{2} * 2 + b\).

Step 3: Solve for the y-intercept \(b\)

After substitution, calculation yields \(-6 = -3 + b\). Rearranging the equation to solve for \(b\), we get \(b = -6 + 3\). Therefore, \(b = -3\).