Question

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

Answer 1

`y=-(1)/(5) x-5`

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:
`(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=-(1)/(5) x+b`

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

Therefore:
`-4=-(1)/(5) (-5)+b\\-4=(5)/(5) +b\\-4=1+b\\b=-4-1=-5`

Then our final answer is that the new line should have the form:
`y=-(1)/(5) x-5`