Question

Find an equation of the line through (3,5) and parallel to y = 3x -7. Write the equation using function notation

Answer 1

Given:

Equation of line is $y=3x-7$.

To find:

The equation of line which is parallel line to $y=3x-7$ and passes through (3,5) in function notation.

Solution:

Slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept.

On comparing the equation $y=3x-7$ with slope intercept form, we get

$m=3$

So, slope of given line is 3.

Slope of parallel lines are same. Thus, the slope of parallel line is also 3.

Point slope form of a line is

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

where, m is slope.

The parallel line passes through (3,5) with slope 3. So, the equation of line is

$y-5=3(x-3)$

$y-5=3x-9$

Add 5 on both sides.

$y=3x-9+5$

$y=3x-4$

Function notation of this equation is

$f(x)=3x-4$

Therefore, the equation equation in function notation is $f(x)=3x-4$.