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Chapter 2: Problem 84

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

Short Answer

Expert verified
The y-intercept of the line is -3.

Step by step solution

01

Write down the given information

We know that a point on the line is (2,-6) and the slope of the line is -3/2. So in the equation \(y = mx + b\), we have \(y = -6\), \(m = -3/2\), and \(x = 2\).
02

Substitute into the slope-intercept form

Our goal is to find \(b\), the y-intercept. So if we plug these values into the slope-intercept equation, we get \(-6 = -3/2 * 2 + b\).
03

Calculate the y-intercept

Now simplify the equation to calculate the value of \(b\). The equation simplifies to \(-6 = -3 + b\). When we add 3 to both sides, we get \(b = -6 + 3 = -3\).

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