Answer:
[tex]y=-3x+5[/tex]
Step-by-step explanation:
The equation for slope is:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can substitute the given coordinates into the equation:
[tex]Slope=\frac{3-0}{\frac{2}{3}-\frac{5}{3}}=\frac{3}{\frac{2-5}{3}}=\frac{3}{\frac{-3}{3}}=\frac{3}{-1}=-3[/tex]
The slope is -3
The equation for a line is:
[tex]y=mx+b[/tex]
m: slope
b: y-intercept
x, y: (x, y) coordinate pair
Now, plug in the slope and one of the (x, y) coordinate pairs to solve for the y-intercept.
[tex]y=mx+b\\y=-3x+b\\0=-3(\frac{5}{3})+b\\0=\frac{-15}{3}+b\\0=-5+b\\$Add 5 to both sides\\b=5[/tex]
Therefore the equation is:
[tex]y=-3x+5[/tex]
