How to write the slope intercept form of the equation of the line described; (-2,-1) parallel to y=-3/2x-1?

Jul 29, 2017

See a solution process below:

Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

$y = \textcolor{red}{- \frac{3}{2}} x - \textcolor{b l u e}{1}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Therefore the slope of this line is: $\textcolor{red}{m = - \frac{3}{2}}$

Parallel lines by definition have the same slope. Therefore, we can substitute this slope into the formula giving:

$y = \textcolor{red}{- \frac{3}{2}} x + \textcolor{b l u e}{b}$

We have been given a point on the parallel line so we can substitute the values of the point for $x$ and $y$ and solve for $\textcolor{b l u e}{b}$

$y = \textcolor{red}{- \frac{3}{2}} x + \textcolor{b l u e}{b}$ becomes:

$- 1 = \left(\textcolor{red}{- \frac{3}{2}} \times - 2\right) + \textcolor{b l u e}{b}$

$- 1 = \textcolor{red}{3} + \textcolor{b l u e}{b}$

$- 3 - 1 = - 3 + \textcolor{red}{3} + \textcolor{b l u e}{b}$

$- 4 = 0 + \textcolor{b l u e}{b}$

$- 4 = \textcolor{b l u e}{b}$

We can now substitute the slope and y-intercept into the formula giving:

$y = \textcolor{red}{- \frac{3}{2}} x + \textcolor{b l u e}{- 4}$

$y = \textcolor{red}{- \frac{3}{2}} x - \textcolor{b l u e}{4}$