Question

Write the slope-intercept form of the equation of the line; (-5,-4) and prep. To y equals 5x plus 1

Answer 1

Answer:

$y=-\frac{1}{5} x-5$

Step-by-step explanation:

The given line is defined by:  $y=5x+1$, where we see that the slope is 5 and the y-intercept 1.

In order to find a line perpendicular to the given one, we need it to have a slope that is the "opposite of the reciprocal" of the given slope.

"Opposite" means it would have its sign inverted (in our case from positive to negative); and "reciprocal means that instead of 5, it would be its reciprocal: $\frac{1}{5}$.

We can write this new line with such slope, and try to find its y-intercept (b) by using the given condition that requires it to go through the point (-5,-4) on he plane:

$y=-\frac{1}{5} x+b$

we require then that when $x=-5$, the value of $y=-4$.

Therefore: $-4=-\frac{1}{5} (-5)+b\\-4=\frac{5}{5} +b\\-4=1+b\\b=-4-1=-5$

Then our final answer is that the new line should have the form: $y=-\frac{1}{5} x-5$