What is the equation of the line with slope $m = - \frac{11}{3}$ $m= -11/3$ that passes through $(\frac{13}{15}, - \frac{23}{24})$ $(13/15,-23/24)$ ?

Question

1584 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-15T18:16:31

$y = - \frac{11}{3} x + \frac{799}{360}$ $y=-11/3x+799/360$

Recall that the general equation of a line is:

$color(blue)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))$

where:
$y=$ y-coordinate
$m=$ slope
$x=$ x-coordinate
$b=$ y-intercept

Determining the Equation
$1$ . Start by substituting $color(orange)(m=-11/3)$ into the formula.

$y=mx+b$

$y=color(orange)(-11/3)x+b$

$2$ . Since you are also given the coordinate, $(color(purple)(13/15),color(teal)(-23/24))$ , substitute it into the equation as well.

$color(teal)(-23/24)=color(orange)(-11/3)color(purple)((13/15))+b$

$3$ . Solve for the unknown value of the variable, $b$ .

$-23/24=-143/45+b$

$b=799/360$

$4$ . Rewrite the equation.

$color(green)(|bar(ul(color(white)(a/a)y=-11/3x+799/360color(white)(a/a)|)))$

What is the equation of the line with slope m= -11/3 m=−113 m= -11/3 that passes through (13/15,-23/24) (1315,−2324) (13/15,-23/24) ?