Question

question
use point - slope form to write the equation of a line that passes through the point ((-14, -1)) with slope (\frac{1}{3}).
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answer attempt 1 out of 2

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.

Step2: Identify values of \(x_1\), \(y_1\) and \(m\)

We are given the point \((- 14,-1)\), so \(x_1=-14\), \(y_1 = - 1\) and the slope \(m=\frac{1}{3}\).

Step3: Substitute values into the formula

Substitute \(x_1=-14\), \(y_1=-1\) and \(m = \frac{1}{3}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-1)=\frac{1}{3}(x - (-14))\).
Simplify the left - hand side and the right - hand side: \(y + 1=\frac{1}{3}(x + 14)\).

Answer:

\(y + 1=\frac{1}{3}(x + 14)\)