Write an equation of the line that passes through (2,-5) and is parallel to the line 2y=3x+10.

Answer 1

To find the equation of a line, we need a point and a slope. We're given a point, and we can easily get the slope. First let's solve 2y = 3x + 10 for y so we can get the slope (recall that y = mx + b is the slope-intercept form, and m is your slope).

2y = 3x + 10 --> almost there already, just divide everything by 2 to get y by itself.

y = 3/2x + 5 --> now you have it in the y=mx + b form, so your slope is 3/2

They asked for the parallel line, remember parallel lines have the same slope, therefore you use the same slope.

Now we know that our slope is m = 3/2 and our point is (2, -5)

You can always find the equation of a line using the Point-Slope Formula:

y - y₁ = m(x - x₁) --> our x₁ is 2 and our y₁ is -5, and slope is 3/2

y - (-5) = 3/2(x - 2) --> Be careful when you have minus a negative number, like we do here. It becomes:

y + 5 = 3/2(x - 2) --> now distribute the 3/2

y + 5 = 3/2x - 6/2

y + 5 = 3/2x - 3 --> now we can subtract 5 from both sides to get it into slope intercept form.

y = 3/2x - 8 --> This is the equation of a line that is parallel to 2y=3x+10 & passes through (2, -5)