Answer:
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]
Step-by-step explanation:
First we need to find the slope of the line. We can plug in both coordinates in to the slope formula.
The slope formula is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
So I will use (-3,4) as the first coordinate, and (7,-1) as the second coordinate.
x₁ = -3
y₁ = 4
x₂ = 7
y₂= -1
I will plug in these values to find the slope.
[tex]m=\frac{y2-y1}{x2-x1}\\\\m=\frac{-1-4}{7-(-3)}\\\\m=\frac{-5}{10}\\\\m=-\frac{1}{2}[/tex]
Now that we know the slope is -1/2, we can plug in the slope and a point into the point slope equation. Then we can solve for y.
[tex]y-y_{1} =m(x-x_{1} )\\\\y-4==-\frac{1}{2}(x-(-3))\\\\y-4=-\frac{1}{2}x-\frac{3}{2}\\\\ y=-\frac{1}{2}x+\frac{5}{2}[/tex]
I have attached an image of what this graph should look like. Since the slope is -1/2, the y value should decrease by 1/2 every time you move over by 1 on the x axis. And since the equation says "+5/2" we know we have to shift the graph up by 5/2. The y-intercept will be 5/2.
I added another image that shows how to graph an equation using the equation y=mx+b
