Question

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

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