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Chapter 2: Problem 83

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

Short Answer

Expert verified
The y-intercept is 5.

Step by step solution

01

Write down the given point and slope

The given point \((x_0, y_0)\) is \( (3, -1)\) and the slope \(m\) is \(-2\).
02

Use the point-slope form of the line's equation

The equation of a line in point-slope form is \(y - y_0 = m(x - x_0)\). Substituting the given point and slope into this equation gives the equation of the line: \(y - (-1) = -2(x - 3)\).
03

Simplify to find the y-intercept

Expand and simplify the equation to get it in the form \(y = mx + b\), where \(b\) is the y-intercept. Doing this gives: \(y + 1 = -2x + 6\), and further simplifying gives: \(y = -2x + 5\). Here, \(b=5\) is the y-intercept.

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