Slope-intercept form is the common format used for linear equations. It looks like y=mx+by=mx+b, with mm being the slope, xx being the variable, and bb is the yy-intercept. We need to find the slope and the yy-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)y2−y1x2−x1. The xxs and yys 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 22s and which is the 11s. It makes no difference which one is which, but I set mine up like this: (-5-1)/(-3--4)−5−1−3−−4. This simplifies down to -6/1−61, or just -6−6. So our slope is -6−6. Now let's move on to the yy-intercept.
I'm sure there are other ways to find the yy-interccept (the value of yy when x=0x=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.
