Question

13. Write the equation of the line perpendicular to
5y = 3x + 25 but passing through (-4,-1)

Answer 1

y = -
`(5)/(3)`x - -
`(23)/(3)`

Explanation:

First, let's divide both sides by 5 to get the first equation into the form y = mx + b. We get y =
`(3)/(5)`x + 5. The m value,
`(3)/(5)`, is the slope and the b value, 5, is the y-intercept of this line.

When a line is perpendicular to another line, the slopes must multiply to get -1. In other words, the slopes must be a negative reciprocal of each other. Since the slope of the original line is
`(3)/(5)`, we know that the slope of the line perpendicular to that is -
`(5)/(3)`.

Then, since we know x, y, and m of the second equation, we can substitute those three values into the equation, y = mx + b, to find the y-intercept (b).

-1 = (-
`(5)/(3)`)(-4) + b

-1 =
`(20)/(3)` + b

b = -
`(23)/(3)`

After plugging in the values of m and b we calculated, we get the equation for the line perpendicular to the original line: y = -
`(5)/(3)`x -
`(23)/(3)`.