One way we can organize a linear equation is in standard form:
[tex]Ax+By=C[/tex]
Another way we can organize a linear equation is in point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We're given:
We only need the point-slope form equation to find the stand form of the equation for this line. All we have to do is rearrange the numbers to get them in the right places.
[tex]y+7=-\dfrac{5}{2}(x-10)[/tex]
⇒ First, multiply both sides by 2 to get rid of the fraction:
[tex]2y+14=-5(x-10)[/tex]
⇒ Now, open up the parentheses:
[tex]2y+14=-5x+50[/tex]
⇒ Move -5x to the other side:
[tex]5x+2y+14=50[/tex]
⇒ Move 14 to the other side:
[tex]5x+2y=50-14[/tex]
⇒ Combine like terms:
[tex]5x+2y=36[/tex]
[tex]5x+2y=36[/tex]
