Question

2) Find the equation of a line that is parallel to y = 5x + 7 and passes through (4, 3)

Answer 1

y=5x-17

Explanation:

Given the equation of the line: y=5x+7.

We want to find a line parallel to it that passes through (4,3).

Slopes are used to determine if two lines are parallel or not.

First, we determine the slope of y=5x+7 with the slope-intercept form of a line.

`\begin{gathered} y=mx+b \\ y=5x+7 \\ \implies\text{Slope,m = 5} \end{gathered}`

Two lines are parallel if they have the same slope.

• Therefore, the slope of the new line = 5

Since the two lines are parallel, the new line has the following properties:

• Slope, m =5

,

• Point, (x1,y1)=(4,3)

We then use these to find the required equation of the line.

Substitute the slope and point into the point-slope form of a line.

`\begin{gathered} y-y_1=m(x-x_1) \\ \implies y-3=5(x-4) \end{gathered}`

We then rewrite it in the slope-intercept form.

The required equation of the line is y=5x-17.