Question

What is an equation of the line that passes through the point (8, 2) and is parallel to the line 5x - 4y = 36?​

Answer 1

Answer:

$y=\frac{5}{4}x-8$

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 the line crosses the y-axis)
• Parallel lines always have the same slopes and different y-intercepts

1) Determine the slope (m)

$5x - 4y = 36$

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

Subtract 5x from both sides

$5x - 4y-5x = -5x+36\\-4y=-5x+36$

Divide both sides by -4

$y=\frac{5}{4} x-9$

Now, we can see that $\frac{5}{4}$ is in the place of m, making it the slope. Because parallel lines have the same slopes, the slope of the line we're solving for is therefore $\frac{5}{4}$. Plug this into $y=mx+b$:

$y=\frac{5}{4}x+b$

2) Determine the y-intercept (b)

$y=\frac{5}{4}x+b$

Plug in the given point (8,2) and solve for b

$2=10+b$

Subtract 10 from both sides

$2-10=10+b-10\\-8=b$

Therefore, the y-intercept is -8. Plug this back into $y=\frac{5}{4}x+b$:

$y=\frac{5}{4}x-8$

I hope this helps!