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Answer:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]
Step-by-step explanation:
The point-slope form of an equation for a line is y = mx + b (m is the slope; b is the y-intercept).
First, find the slope using the two given points.
[tex]m=\frac{y_2 - y_1}{x_2-x_1}=\frac{3-0}{4-(-5)}=\frac{3}{9}=\frac{1}{3}[/tex]
At this stage, you know the slope and need to find the y-intercept. Plug in one of the points (either one) into the equation. Let's use (-5, 0).
[tex]y=\frac{1}{3}x+b\\0=\frac{1}{3}(-5)+b\\0=-\frac{5}{3}+b\\\frac{5}{3}=b[/tex]
The equation for the line is [tex]y=\frac{1}{3}x+\frac{5}{3}[/tex].
You can check for errors by putting in the point you didn't use...
Check to make sure the point (4, 3) satisfies the equation.
[tex]3=\frac{1}{3}(4)+\frac{5}{3}\\3=\frac{4}{3}+\frac{5}{3}\\3=\frac{9}{3}[/tex] True!