Question

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

Answer 1

Answer:

$y = 1.5x - 8$

Step-by-step explanation:

Step 1:  Solve for y in the first equation

$2y = 3x + 10$

$\frac{2y}{2}=\frac{3}{2}x + \frac{10}{2}$

$y = 1.5x + 5$

Step 2:  Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1.5 which means that our slope is also going to be 1.5.  We also know that our line crosses the point (2, -5) which means that we can use the point slope form to determine our equation

Point Slope Form → $(y-y_1) = m(x - x_1)$

Step 3:  Plug in the information and solve

$(y-(-5)) = 1.5(x - 2)$

$y + 5 = 1.5x -3$

$y + 5 - 5 = 1.5x -3 - 5$

$y = 1.5x - 8$

Answer: $y = 1.5x - 8$

Answer 2

Answer:

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.