Slope-intercept form is the common format used for linear equations. It looks like #y=mx+b#, with #m# being the slope, #x# being the variable, and #b# is the #y#-intercept. We need to find the slope and the #y#-intercept to write this equation.
In order to find the slope, we use something called the slope formula. It is #(y_2-y_1)/(x_2-x_1)#. The #x#s and #y#s refer to the variables within coordinate pairs. Using the pairs we are given, we can find the slope of the line. We choose what set is the #2#s and which is the #1#s. It makes no difference which one is which, but I set mine up like this: #(-5-1)/(-3--4)#. This simplifies down to #-6/1#, or just #-6#. So our slope is #-6#. Now let's move on to the #y#-intercept.
I'm sure there are other ways to find the #y#-interccept (the value of #y# when #x=0#), but I'm going to use the table method.
#color(white)(-4)X color(white)(......)| color(white)(......) color(white)(-)Y#
#color(white)(.)-4 color(white)(......)| color(white)(......) color(white)(-)1#
#color(white)(.)-3 color(white)(......)| color(white)(......) color(white)()-5#
#color(white)(.)-2 color(white)(......)| color(white)(......) color(white)()-11#
#color(white)(.)-1 color(white)(......)| color(white)(......) color(white)()-17#
#color(white)(.-)0 color(white)(......)| color(white)(......) color(white)()-23#
When #x# is #0#, #y# is #-23#. That's our #y#-intercept. And now we have all the pieces we need.
#y=mx+b#
#y=-6x-23#. Just to be safe, let's graph our eqaution and see if we hit the points #(-3, -5)# and #(-4, 1)#.
graph{y=-6x-23}
And it does! Great work.
