Question

Line a can be described by the equation 3x - 4y = 8.

Answer 1

Given:

Equation of a line is

$3x-4y=8$

To find:

The equation of line in slope intercept form that is parallel to line a and goes through point (24, 6).

Solution:

If a linear equation is $ax+by+c=0$, then

$Slope=-\dfrac{a}{b}$

In the equation $3x-4y=8$, a=3 and b=-4, thus the slope of the line is

$Slope=-\dfrac{3}{-4}$

$Slope=\dfrac{3}{4}$

We know that, slope of two parallel lines are same. So, slope of parallel line is

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

The parallel line passes through (24, 6) and have slope $m=\dfrac{3}{4}$, so the equation of line is

$y-6=\dfrac{3}{4}(x-24)$

$y-6=\dfrac{3}{4}(x)-\dfrac{3}{4}(24)$

$y-6=\dfrac{3}{4}(x)-18$

Add 6 on both sides.

$y=\dfrac{3}{4}(x)-18+6$

$y=\dfrac{3}{4}(x)-12$

Therefore, the equation of parallel line in slope intercept form is $y=\dfrac{3}{4}(x)-12$.