Question

What is the equation of a line that passes through the point (7,0) and is parallel to the line represented by the equation y= 2.5x + 3.5

Answer 1

We have the following:

The line passes through the coordinates (7, 0):

The line is parallel to the equation:

`\begin{gathered} y=2.5x+3.5 \\ m(parallel)=2.5 \end{gathered}`

We will find the equation of the line as shown below:

I. Find the slope of the line, we have:

`\begin{gathered} m(parallel)=2.5 \\ m(parallel)\cong m=2.5 \\ \Rightarrow m=2.5 \\ \\ \therefore m=2.5 \end{gathered}`

II. We will use the point-slope equation to obtain the equation of the line as shown below:

`\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(7,0) \\ m=2.5 \\ y-0=2.5(x-7) \\ y=2.5x-17.5 \\ \\ \therefore y=2.5x-17.5 \end{gathered}`

T