Question

I need help understanding this problem. any help would be greatly appreciated

Answer 1

The given point is (12,6) and the given line equation is y=1/4 x-12.

It is required to find the equation of the line parallel to the line whose equation is given and passes through the given point.

Recall that the Equation of a Line in point-slope form is given as:

`y-y_1=m(x-x_1)`

Where m is the slope of the line and (x₁,y₁) is the point the line passes through.

Recall also that the slopes of parallel lines are equal.

The slope-intercept form of the equation of a line with slope m and y-intercept b is:

`y=mx+b`

Compare with the equation of the given line, it follows that m=1/4.

Hence, the slope of the given line is 1/4.

Since the required line whose equation is to be found is parallel to the given line, it must have the same slope.

Substitute m=1/4 and the point (x₁,y₁)=(12,6) into the point-slope form of the equation of a line:

`\begin{gathered} y-6=(1)/(4)(x-12) \\ \Rightarrow y-6=(1)/(4)x-(1)/(4)(12) \\ \Rightarrow y-6=(1)/(4)x-3 \\ \Rightarrow y=(1)/(4)x-3+6 \\ \Rightarrow y=(1)/(4)x+3 \end{gathered}`

The required equation is shown above.