Question

WRITE an equation of the line that passes through the given point and is PARALLEL to the given line.


(10, -12), 3x + 4y = 1

Answer 1

Answer:

$y=-\frac{3}{4}x-\frac{9}{2}$

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)

$3x + 4y = 1$

Rearrange the given equation into slope-intercept form (this will help us determine m)

Subtract 3x from both sides to isolate 4y

$3x + 4y-3x = -3x+1\\4y= -3x+1$

Divide both sides by 4 to isolate y

$y= -\frac{3}{4} x+\frac{1}{4}$

Now, we can identify that $-\frac{3}{4}$ is the slope of the line. Parallel lines have the same slope, so this would also be the slope of the line we're solving for. Plug this into $y=mx+b$:

$y=-\frac{3}{4}x+b$

2) Determine the y-intercept (b)

$y=-\frac{3}{4}x+b$

Plug in the given point (10,-12) and solve for b

$-12=-\frac{3}{4}(10)+b\\-12=-\frac{3}{2}(5)+b\\-12=-\frac{15}{2}+b$

Add $\frac{15}{2}$ to both sides to isolate b

$-12+\frac{15}{2}=-\frac{15}{2}+b+\frac{15}{2}\\-12+\frac{15}{2}=b\\-\frac{9}{2} =b$

Therefore, the y-intercept is $-\frac{9}{2}$. Plug this back into $y=-\frac{3}{4}x+b$:

$y=-\frac{3}{4}x-\frac{9}{2}$

I hope this helps!