Write an equation of the line that passes through the point (-2, 5) and is parallel to the line 2x − 3y = 12.

Now, you can determine if a line is parallel or perpendicular by its slope. parallel has the same slope and perpendicular has the negative reciporical, which basically means negative 1 divided by the slope.

So if you slope was 3 perpendicular would be -1/3. if the slope is a fraction you can just flip the fraction and make it negative. so if the slope is -2/3 a perpendicular slope would be 3/2, making a negative number negative makes it positive.

Now you start with 2x - 3y = 12. To find the slope I like putting it in slope intercept form. basically somethign that looks liek y = mx + b. to do that just use algebra on what you have to get y by itself. here is how I would do that.

2x - 3y = 12 first subtract 2x from both sides

-3y = 12 - 2x Now divide both sides by -3

y = 12/-3 - (2x)/3 Now simplify

y = -4 + 2/3 x Now rarrange to make it look like I said, basically you want the x first.

y = 2/3 x - 4

There, so the slope is 2/3. A parallel line will have the same slope.

To make the equation of a line you want one point and the slope. Well we have that, the point is (-2,5) and the slope is 2/3.

To find a line you set up the point slope form. that is y - y1 = m(x - x1) where m is the slope and x1 and y1 are the coordinates of the point you need. I will plug all that in.

y - y1 = m(x - x1)

y - 5 = (2/3)(x - (-2)) Now solve

y - 5 = (2/3)x + 4/3

y = (2/3)x + 19/3

So that is the equation of a line parallel to 2x - 3y = 12 that passes through (-2, 5)