Question

What is an equation of the line that passes through the point (3,6)(3,6) and is parallel to the line 4x-3y=214x−3y=21?

Answer 1

Question:

What is an equation of the line that passes through the point (3,6) and is parallel to the line 4x-3y=21

Answer:

The equation of the line that passes through the point (3,6) and is parallel to the line 4x-3y=21 is:

$y = \frac{4}{3}x + 2$

Solution:

Given that line passes through the point (3,6) and is parallel to the line 4x-3y=21

The equation of line in slope intercept form is given as:

y = mx + c ------- eqn 1

Where, "m" is the slope and "c" is the y intercept

Given equation is:

4x - 3y = 21

Rearrange,

3y = 4x - 21

$y = \frac{4}{3}x - \frac{21}{3}\\\\y = \frac{4}{3}x - 7$

On comparing above equation with eqn 1,

$m = \frac{4}{3}$

We know that slopes of parallel lines are same

Therefore, slope of line parallel to the line 4x - 3y = 21 is 4/3

Substitute m = 4/3 and (x, y) = (3, 6) in eqn 1

$6 = \frac{4}{3} \times 3 + c\\\\6 = 4 + c\\\\c = 2$

Substitute c = 2 and m = 4/3 in eqn 1

$y = \frac{4}{3}x + 2$

Thus the equation of line is found