Question

A line passes through the point (-2,5) and has a slope of 2/3.points A(x,3) and B(-2,y) lie on the line

Answer 1

Given:

A line passes through the point (-2,5) and has a slope of 2/3. points A(x,3) and B(-2,y) lie on the line.

Required:

We need to find the value of x and y.

Step-by-step explanation:

Consider the slope point line equation.

`y-y_1=m(x-x_1)`

Substitute known values on the formula.

`y-5=(2)/(3)(x-(-2))`
`Subs\text{titue }x_1=-2,y_1=5,\text{ and }m=(2)/(3)\text{ in the equation.}`

`3-5=(2)/(3)(x+2)`
`-2=(2)/(3)(x+2)`
`-2*(3)/(2)=(3)/(2)*(2)/(3)(x-(-2))`
`-3-2=x+2-2`
`x=-5`

Substitute x =-2 in the line equation to find the value of y.

`y-5=(2)/(3)(-2-(-2))`
`y-5=(2)/(3)(0)`
`y-5=0`
`y-5+5=0+5`
`y=5`

Final answer:

x=-5 and y =5