Question

Answer and please show the work.​

Answer 1

`y=\displaystyle(1)/(2) x-3`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

`m=\displaystyle(y_2-y_1)/(x_2-x_1)` where two points on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (4,-1) and (0,3)

`m=\displaystyle(-1-(-3))/(4-0)\\\\m=\displaystyle(2)/(4)\\\\m=\displaystyle(1)/(2)`

Therefore, the slope of the line is
`\displaystyle(1)/(2)`. Plug this into
`y=mx+b` :

`y=\displaystyle(1)/(2) x+b`

2) Determine the y-intercept (b)

`y=\displaystyle(1)/(2) x+b`

The y-intercept occurs when x=0. Because we're given that (0,-3), the y-intercept is therefore -3.

`y=\displaystyle(1)/(2) x-3`

I hope this helps!