Question

How do you write an equation of a line with slope -3 and y – intercept -2?

Answer 1

We know that the general form of the equation of straight line with slope “m” and y intercept “c” is equal to: $y=mx+c$. In the above problem, we are asked to write the equation of a straight line with slope -3 and y – intercept -2 so we are going to use the general form of equation of straight line which we have just described. Substituting “m” as -3 and “c” as -2 in $y=mx+c$ will give us the equation of straight line.

Complete step by step answer:
In the above problem, we have given the slope -3 and y – intercept -2 and are asked to find the equation of the straight line. We know that the general form of equation of straight line with slope “m” and y – intercept “c” is equal to:
$y=mx+c$
Now, to write the equation of line with slope -3 and y - intercept -2 we are going to substitute the value of “m” as -3 and “c” as -2 in the above general form of straight line.
$y=\left( -3 \right)x+\left( -2 \right)$
We know that if we multiply “+” sign with “-“ sign we get “-“ sign so using this concept in the R.H.S of the above equation we get,
$y=-3x-2$
Rearranging the terms by adding $3x\And 2$ on both the sides of the above equation we get,
$y+3x+2=-3x-2+3x+2$
In the above equation, $-3x$ will be cancelled out with $+3x$ and -2 will be cancelled out with +2 so all the terms on R.H.S of the above equation will vanish.
$y+3x+2=0$

Hence, we have found the equation of straight line as $y+3x+2=0$.

Note: You can check the equation of line that you have found is correct or not by substituting “x” as 0 in the given equation to see what value of “y” you are getting,
Substituting x as 0 in $y+3x+2=0$ we get,
$\begin{aligned} & y+3\left( 0 \right)+2=0 \\\ & \Rightarrow y+0+2=0 \\\ & \Rightarrow y=-2 \\\ \end{aligned}$
As you can see that the value of y is -2. And this y equals -2 is the y – intercept of the line. It is given above that y intercept is -2. Hence, the equation of line that we have found is correct.