Chapter 4, Problem 4MCQ

To determine

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

Answer to Problem 4MCQ

  $y=2x+10$

Explanation of Solution

Given:

Line passing through the points $\left(-3,4\right),\left(1,12\right)$ .

Concept used:

Equation of a line passing through the points $\left(x_1,y_1\right)\&\left(x_2,y_2\right)$ is $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ .

Calculation:

Given,

  $\left(x_1,y_1\right)=\left(-3,4\right)\&\left(x_2,y_2\right)=\left(1,12\right)$

Now the equation of the line is,

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ \Rightarrow y-4=\frac{12-4}{1-\left(-3\right)}\left(x-\left(-3\right)\right)\\ \Rightarrow y-4=\frac{8}{4}\left(x+3\right)\\ \Rightarrow y-4=2\left(x+3\right)\\ \Rightarrow y-4=2x+6\\ \Rightarrow y=2x+6+4\\ \Rightarrow y=2x+10\end{array}$