Question

use point - slope form to write the equation of a line that passes through the point (-2, -10) with slope \\(\frac{1}{3}\\).
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 that the point \((x_1,y_1)=(-2,-10)\) and the slope \(m = \frac{1}{3}\).

Step3: Substitute values into the formula

Substitute \(x_1=-2\), \(y_1 = - 10\) and \(m=\frac{1}{3}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-10)=\frac{1}{3}(x - (-2))\).
Simplifying the left - hand side and the right - hand side, we have \(y + 10=\frac{1}{3}(x + 2)\).

Answer:

\(y + 10=\frac{1}{3}(x + 2)\)