Answer:
![y=-\frac{4}{7}x+4\frac{1}{7}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B4%7D%7B7%7Dx%2B4%5Cfrac%7B1%7D%7B7%7D)
Step-by-step explanation:
So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).
Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.
Slope of the line: m= ![\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B1%7D%20-%20y_%7B2%7D%20%20%7D%7Bx_%7B1%7D%20-%20x_%7B2%7D%20%20%7D%20%3D%20%5Cfrac%7B7-3%7D%7B-5-2%7D%20%3D%20%5Cfrac%7B4%7D%7B-7%7D%3D%20-%5Cfrac%7B4%7D%7B7%7D)
If you haven't been taught how to find the slope of a line I recommend you find out.
Substitute the slope into the equation.
![y=-\frac{4}{7} x+b\\](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B4%7D%7B7%7D%20x%2Bb%5C%5C)
Now, we will solve for the 'b,' or y intercept.
We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.
![y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B4%7D%7B7%7D%20x%2Bb%5C%5C%5C%5C3%3D-%5Cfrac%7B4%7D%7B7%7D%20%2A2%2Bb%5C%5C%5C%5C3%3D-%5Cfrac%7B8%7D%7B7%7D%20%2Bb%5C%5Cb%3D3%2B%5Cfrac%7B8%7D%7B7%7D%20%5C%5Cb%3D%5Cfrac%7B21%7D%7B7%7D%2B%5Cfrac%7B8%7D%7B7%7D%3D%5Cfrac%7B29%7D%7B7%7D%20%3D4%5Cfrac%7B1%7D%7B7%7D%20%5C%5Cb%3D4%5Cfrac%7B1%7D%7B7%7D)
Last step: substitute the slope and y intercept into y=mx+b.
![y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-%5Cfrac%7B4%7D%7B7%7Dx%2B4%5Cfrac%7B1%7D%7B7%7D)
That is the answer to this problem.
I hope this helps.