Given:
[tex]6x+3y=12[/tex]
[tex]2x-6y=18[/tex]
[tex]5x+2y=16[/tex]
[tex]6x-8y=-24[/tex]
To find:
The slope intercept form of each equation.
Solution:
We know that, slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
The first equation is
[tex]6x+3y=12[/tex]
Subtract 6x from both sides.
[tex]3y=12-6x[/tex]
Divide both sides by 3.
[tex]y=\dfrac{12-6x}{3}[/tex]
[tex]y=\dfrac{12}{3}-\dfrac{6x}{3}[/tex]
[tex]y=4-2x[/tex]
[tex]y=-2x+4[/tex]
Therefore, the slope intercept form of first equation is [tex]y=-2x+4[/tex].
Similarly,
[tex]2x-6y=18[/tex]
[tex]-6y=18-2x[/tex]
[tex]y=\dfrac{18-2x}{-6}[/tex]
[tex]y=-3+\dfrac{1}{3}x[/tex]
[tex]y=\dfrac{1}{3}x-3[/tex]
Therefore, the slope intercept form of second equation is [tex]y=\dfrac{1}{3}x-3[/tex].
[tex]5x+2y=16[/tex]
[tex]2y=16-5x[/tex]
[tex]y=\dfrac{16-5x}{2}[/tex]
[tex]y=8-\dfrac{5}{2}x[/tex]
[tex]y=-\dfrac{5}{2}x+8[/tex]
Therefore, the slope intercept form of third equation is [tex]y=-\dfrac{5}{2}x+8[/tex].
[tex]6x-8y=-24[/tex]
[tex]-8y=-24-6x[/tex]
[tex]y=\dfrac{-24-6x}{-8}[/tex]
[tex]y=\dfrac{-24}{-8}-\dfrac{6x}{-8}[/tex]
[tex]y=3+\dfrac{3}{4}x[/tex]
[tex]y=\dfrac{3}{4}x+3[/tex]
Therefore, the slope intercept form of fourth equation is [tex]y=\dfrac{3}{4}x+3[/tex].
