y=mx+b where m= slope, and b= y-intercept

You need to determine m and b, by using the information you were given: the equation of a perpendicular line and a point, That is all that you need to answer this question.

First, the tricky party. You have to know that perpendicular lines have slopes that are negative recipricol of each other. (negative recipricol means that when you multiply them together you get -1). Since you are given one line with a slope of 2/3, a line that is perpendicular to that must have a slope of -3/2 (2/3 X -3/2 = -1)). So you have the first part of your answer, your slope, m= -3/2

Plug that into the formula for and you have:

y=-3/2x +b

This will give you all lines parallel or equal to the line you want.

Now you have to find b.

You are given a point (2,5). To find a formula for a line through a specific point, you just plug in the coordinates (X,Y) into the equation to see if it’s true:

5 = -3/2(2) + b now simplify:

5= -3 + b If we solve for b, we get that value that makes the equation true for the point.

b=8

So now you have m and you have b, plug these into your equation in slope intercept format and you get:

y = -3/2x + 8

Double check, does the line go through (2,5)? Plug 2 in for X and 5 in for Y:

5= -3/2 (2) + 8 True?

5 = -3 + 8 Yes!

Hope that helps.

** Note: edited to correct error – perpendicular lines have slopes that are negative recipricols – earlier version left out the negative part. sorry, my bad. Good catch mathcat!

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Substitute in your given x and y (2, 5) and the new slope and solve for b in y = mx + b.

5 = (-3/2)(2) + b

5 = -3 + b Add 3 to both sides.

8 = b

Rewrite the equation and you get y = (-3/2)x + 8

This line passes through the point (2,5) as desired and is perpendicular to the original equation.