Question

The equation for line r can be written as y=-1/4x+3. Line s which is parallel to lone r includes the point (-4,3). What is the equation of line s?

Answer 1

Answer:

$y=-\frac{1}{4}x+2$

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 of line S using line R (m)

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

We can identify clearly that the slope of the line is $-\frac{1}{4}$, as it is in the place of m. Because parallel lines always have the same slope, the slope of line S would also be $-\frac{1}{4}$. Plug this into $y=mx+b$:

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

2) Determine the y-intercept of line S (b)

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

Plug in the given point (-4,3) and solve for b

$3=-\frac{1}{4}(-4)+b\\3=1+b$

Subtract 1 from both sides to isolate b

$3-1=1+b-1\\2=b$

Therefore, the y-intercept is 2. Plug this back into $y=-\frac{1}{4}x+b$:

$y=-\frac{1}{4}x+2$

I hope this helps!