Question

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

Answer 1

`y=-3x+5`

Explanation:

The equation for slope is:

`Slope=(y_2-y_1)/(x_2-x_1)`

We can substitute the given coordinates into the equation:

`Slope=(3-0)/((2)/(3)-(5)/(3))=(3)/((2-5)/(3))=(3)/((-3)/(3))=(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((5)/(3))+b\\0=(-15)/(3)+b\\0=-5+b\\$Add 5 to both sides\\b=5`

Therefore the equation is:

`y=-3x+5`