Question

Write an equation for a line going through the point (-5, -10) that is parallel to theline 1/5x-1/6y = 7.

Answer 1

Two lines are parallel if they have the same slope. In order to better visualize the slope of the line we will express it in the slope-intercept form, which is done below:

`\begin{gathered} (1)/(5)x-(1)/(6)y\text{ = 7} \\ (1)/(5)x-7=(1)/(6)y \\ (1)/(6)y\text{ = }(1)/(5)x-7 \\ y\text{ = }(6)/(5)x\text{ - 42} \end{gathered}`

We now know that the slope of the line is 6/5, because in this form the slope is always the number that is multiplying the "x" variable. So we need to find a line of the type:

`h(x)\text{ = }(6)/(5)x+b`

Therefore the only needed variable is "b", which we can find by applying the known point (-5, -10).

`\begin{gathered} -10\text{ = }(6)/(5)\cdot(-5)\text{ + b} \\ -10=-6+b \\ b=-10+6 \\ b=-4 \end{gathered}`

The expression of the line is then:

`h(x)\text{ = }(6)/(5)x-4`