Given:
Equation of a line is
[tex]3x-4y=8[/tex]
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 [tex]ax+by+c=0[/tex], then
[tex]Slope=-\dfrac{a}{b}[/tex]
In the equation [tex]3x-4y=8[/tex], a=3 and b=-4, thus the slope of the line is
[tex]Slope=-\dfrac{3}{-4}[/tex]
[tex]Slope=\dfrac{3}{4}[/tex]
We know that, slope of two parallel lines are same. So, slope of parallel line is
[tex]m=\dfrac{3}{4}[/tex]
The parallel line passes through (24, 6) and have slope [tex]m=\dfrac{3}{4}[/tex], so the equation of line is
[tex]y-6=\dfrac{3}{4}(x-24)[/tex]
[tex]y-6=\dfrac{3}{4}(x)-\dfrac{3}{4}(24)[/tex]
[tex]y-6=\dfrac{3}{4}(x)-18[/tex]
Add 6 on both sides.
[tex]y=\dfrac{3}{4}(x)-18+6[/tex]
[tex]y=\dfrac{3}{4}(x)-12[/tex]
Therefore, the equation of parallel line in slope intercept form is [tex]y=\dfrac{3}{4}(x)-12[/tex].
