Question

Write the equation of the line through the given points : I need help please

Answer 1

Answer:

$y=-3x+5$

Step-by-step explanation:

The equation for slope is:

$Slope=\frac{y_2-y_1}{x_2-x_1}$

We can substitute the given coordinates into the equation:

$Slope=\frac{3-0}{\frac{2}{3}-\frac{5}{3}}=\frac{3}{\frac{2-5}{3}}=\frac{3}{\frac{-3}{3}}=\frac{3}{-1}=-3$

The slope is -3

The equation for a line is:

$y=mx+b$

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.

$y=mx+b\\y=-3x+b\\0=-3(\frac{5}{3})+b\\0=\frac{-15}{3}+b\\0=-5+b\\ Add 5 to both sides\\b=5$

Therefore the equation is:

$y=-3x+5$