Question

Write the equation of a line that is parallel to the given line and passes through the given point.
y=1/3x+1 (-3,4)

Answer 1

Answer:

$y=\frac{1}{3}x +5$

Step-by-step explanation:

Linear equations are typically formatted in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

Parallel lines will always have the same slope. Therefore, this line will also have a slope of $\frac{1}{3}$. Plug this into our equation:

$y=\frac{1}{3} x+b$

2) Determine the y-intercept (b)

To solve for the y-intercept (b), plug the given point (-3,4) into our equation and isolate b.

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

Add 1 to both sides

$4+1=-1+b+1\\5=b$

Therefore, the y-intercept is 5. Plug this back into our original equation with the slope:

$y=\frac{1}{3}x +5$

I hope this helps!