Write the equation of a line that is perpendicular to the line y = 3/4x - 1 and has a y-intercept of (0, 5).

Question

Write the equation of a line that is perpendicular to the line y = 3/4x - 1 and has a y-intercept of (0, 5).Write the equation of a line that is perpendicular to the line y = 3/4x - 1 and has a y-intercept of (0, 5).

Answer 1

Hi Mackenna W

You want the line that is perpendicular to y = (3/4)x - 1 and has a y intercept of (0, 5).

There is a rule for Perpendicular Lines and you can look this up if you want. Perpendicular lines have inverse slopes of opposite signs; they are negative reciprocals of each other.

Your line is given in Slope Intercept Form, y = mx + b where m is the slope and (0, b) is the y intercept. In your given line, m = (3/4) a line perpendicular to your given line would have the following slope, m = (-4/3) it is the inverse of the slope of your given line with the opposite sign. Your perpendicular line in Slope Intercept form can start from there:

y = mx + b

y = (-4/3)x + b

Since we are also given the y intercept (0, 5), we know what b is when x is zero it is 5 so your complete perpendicular line is

y = (-4/3)x + 5

You can check that this line is perpendicular to your given line by graphing them both on the same grid. You can graph them by hand, with graphing calculator, or at desmos,com it is free and easy to use.

I hope this helps and you can go look up the rule for yourself as well as graph your lines to confirm that they are indeed perpendicular to one another.

Answer 2

y = mx + b is the format of the equation that has been given to you.

in this equation format, m is the slope, aka rise over run, aka delta y/delta x.

b is the y-intercept, aka the y when you plug in zero for x. Where the line crosses the y axis.

By definition, parallel lines have the same slope.

So what the question is asking you is:

give us an equation y = mx + b, where the slope is 3/4 and the y-intercept is 5.

Complete this exercise to get the answer. Good luck!