Question

Write an equation of the line that passes through (18,2) and is parallel to the line 3y-x=-12 .

Answer 1

Answer:

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

Step-by-step explanation:

Step 1:  Solve for y in the first equation

$3y - x = -12$

$3y - x + x = -12 + x$

$\frac{3y}{3} = \frac{x}{3} - \frac{12}{3}$

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

Step 2:  Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1/3 which means that our slope is also going to be 1/3.  We also know that our line crosses the point (18, 2) which means that we can use the point slope form to determine our equation

Point Slope Form → $(y-y_1) = m(x - x_1)$

Step 3:  Plug in the information and solve

$(y-2) = \frac{1}{3}(x - 18)$

$y - 2 = \frac{1}{3}x - 6$

$y - 2 + 2 = \frac{1}{3}x - 6 + 2$

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

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