# How do you write the equation in slope intercept form given (1,4) and (2,-5)?

##### 2 Answers

#### Explanation:

Let's find the slope for

Now we need to find

To find that, let's us the point-slope formula again:

Now what? Well, we already know what the slope is. It's

*multiply by #-1# on both sides*

*add #4# on both sides*

Now we have our

Let's graph our equation and make sure it goes through the points

graph{y=-9x+13}

It does! We were right

#### Explanation:

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#

where m represents the slope and b. the y-intercept.

#"to calculate m use the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#

#"the points are " (x_1,y_1)=(1,4),(x_2,y_2)=(2,-5)#

#rArrm=(-5-4)/(2-1)=(-9)/1=-9#

#rArry=-9x+blarr" is the partial equation"#

#"to find b, substitute either of the 2 given points into"#

#"the partial equation"#

#"using " (1,4)#

#4=-9+brArrb=13#

#rArry=-9x+13larrcolor(red)" in slope-intercept form"#