Question

What is the slope of a line parallel to the line whose equation is 3x-18y=-3783x−18y=−378. Fully simplify your answer.

Answer 1

Slope is 1/6

Explanation

What to find? The slope of the line parallel to a given equation

Given equation

`3x\text{ - 18y = -378}`

The slope-intercept form of an equation is given below as

`y\text{ = mx + b}`

Where m is the slope of the line

y is the intercept of the y - axis

The next thing is to rewrite the above equation in the format of the slope-intercept equation

`\begin{gathered} 3x\text{ - 18y = -378} \\ \text{ Isolate -18y by substracting 3x from both sides} \\ 3x\text{ - 3x - 18y = -378 - 3x} \\ -\text{ 18y = -3x - 378} \\ \text{Divide through by -18} \\ \frac{-18y}{-18\text{ }}\text{ = }(-3x)/(-18)\text{ - }(378)/(-18) \\ y\text{ = }(1)/(6)x\text{ + 21} \\ y\text{ = }(1)/(6)x\text{ + 21} \\ \text{ Since y = mx + b} \\ m\text{ = slope} \\ \text{Hence,m = }(1)/(6) \end{gathered}`

For lines that are parallel to each other, the slope remains the same

`m1\text{ = m2}`

Therefore, the slope of the line parallel whose equation is y = 3x - 18y = -378 is 1/6