Answer:
[tex]y=-10x+43[/tex]
Step-by-step explanation:
We need to put this line into slope-intercept form, which is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
The slope is rise over run, how much the [tex]y[/tex] value changes for one [tex]x[/tex] value. This can be found with the equation: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points on the line. Plugging in the first two points:
[tex]m=\frac{3-13}{4-3}=-10/1=-10[/tex]
We know them that [tex]m=-10[/tex]. This gives us for now [tex]y=-10x+b[/tex].
Now, to solve for [tex]b[/tex], plug in any one of the points (I'll use (3,13)):
[tex]13=-10(3)+b[/tex]
[tex]13=-30+b[/tex]
[tex]b=43[/tex]
This gives us the equation [tex]y=-10x+43[/tex].
