# How do you write the equation of a line given m= -5 (2,4)?

Jun 1, 2018

$y = - 5 x + 14$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = - 5$

$y = - 5 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(2,4)" into the partial equation}$

$4 = - 10 + b \Rightarrow b = 4 + 10 = 14$

$y = - 5 x + 14 \leftarrow \textcolor{red}{\text{is the equation of the line}}$

See below:

#### Explanation:

As an alternate way of solving this, we can use the point slope form, which is:

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

Substituting in:

color(blue)(ul(bar(abs(color(black)((y-4)=-5(x-2)))))

We can convert this form into the slope intercept form shown in the other answer:

y-4=-5x+10=>color(blue)(ul(bar(abs(color(black)(y=-5x+14

And also into standard form:

color(blue)(ul(bar(abs(color(black)(5x+y=14

These all describe the same thing - this line:

graph{-5x+14[-20,20,0,20]}