Question

Determine the equation of the line that is parallel to the given line, through the given point.

Answer 1

Answer:

$y=-\frac{3}{2}x+1$

Step-by-step explanation:

Hi there!

What we need to know:

• Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)
• Parallel lines always have the same slope

1) Determine the slope (m)

$3x+2y = 10$

First, we must organize this given equation in slope-intercept form. This will help us identify its slope.

$3x+2y = 10$

Subtract 3x from both sides

$2y = -3x+10$

Divide both sides by 2

$y = -\frac{3}{2} x+5$

Now, we can identify clearly that $-\frac{3}{2}$ is in the place of m in $y=mx+b$, making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for $-\frac{3}{2}$ as well. Plug this number into $y=mx+b$:

$y=-\frac{3}{2}x+b$

2) Determine the y-intercept (b)

$y=-\frac{3}{2}x+b$

Plug in the given point (8,-11) and solve for b

$-11=-\frac{3}{2}(8)+b\\-11=-\frac{24}{2}+b\\-11=-12+b$

Add 12 to both sides

$1=b$

Therefore, the y-intercept of the line is 1. Plug this back into $y=-\frac{3}{2}x+b$:

$y=-\frac{3}{2}x+1$

I hope this helps!