Question

What is the slope and y intercept of $y=-6x-5$?

Answer 1

In the above problem, we have given the equation of a straight line. And the equation is in the following form: $y=-6x-5$. We know that if we have the equation of a straight line in the slope-intercept form which is written as: $y=mx+c$. Then in this slope-intercept form, “m” is the slope of the straight line and “c” is the y – intercept. So, we are going to first of all rearrange the given equation in such a manner so that the given equation will come in this form: $y=mx+c$. Then we compare the two equations and find the value of “m and c”.

Complete step-by-step solution:
The equation given in the above problem is as follows:
$y=-6x-5$
The above equation is the equation for the straight line. And we know that the slope-intercept form for the standard form of straight line is as follows:
$y=mx+c$
In the above equation, “m” is the slope and “c” is the y-intercept. So, we can find the slope and y-intercept for the given straight line equation by first of all rearranging that equation in the above slope-intercept form then compare.
Rearranging the given straight line equation we get,
$y=\left( -6 \right)x+\left( -5 \right)$
We know that multiplication of a positive sign with a negative sign will give a negative sign. Now, comparing the above equation with standard slope-intercept form we get,
$y=\left( -6 \right)x+\left( -5 \right)$
$y=mx+c$
On comparing the above equations, we can find that the value of “m” is equal to -6 and the value of “c” is equal to -5.
Hence, the slope and the y-intercept for the given equation is -6 and -5 respectively.

Note: The above problem will be done in seconds if you know how to write a slope-intercept straight line equation and what is slope and the y-intercept in it so make sure you correctly remember the slope-intercept form of the straight line.