Chapter 4, Problem 3MCQ

To determine

To find the equation of line in slope-intercept form.

Answer to Problem 3MCQ

  $y=\frac{1}{2}x+\frac{1}{2}$

Explanation of Solution

Given:

Line passing through the point $\left(-3,-1\right)$ with slope $\frac{1}{2}$ .

Concept used:

Equation of a line passing through the point $\left(x_1,y_1\right)$ with slope m is $y-y_1=m\left(x-x_1\right)$ .

Calculation:

Given,

  $\left(x_1,y_1\right)=\left(-3,-1\right)\&m=\frac{1}{2}$

Now the equation of the line is,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \Rightarrow y-\left(-1\right)=\frac{1}{2}\left(x-\left(-3\right)\right)\\ \Rightarrow y+1=\frac{1}{2}\left(x+3\right)\\ \Rightarrow y+1=\frac{1}{2}x+\frac{3}{2}\\ \Rightarrow y=\frac{1}{2}x+\frac{3}{2}-1\\ \Rightarrow y=\frac{1}{2}x+\frac{1}{2}\end{array}$