Question

What is an equation of the line that passes through the points (-3,-1) and (6,2)?​

Answer 1

`y=(1)/(3)x`

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 the line crosses the y-axis)

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where two points the line passes through are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (-3,-1) and (6,2)

`=(2-(-1))/(6-(-3))\\=(2+1)/(6+3)\\=(3)/(9)\\=(1)/(3)`

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

`y=(1)/(3)x+b`

2) Determine the y-intercept (b)

`y=(1)/(3)x+b`

Plug in one of the given points and solve for b

`2=(1)/(3)(6)+b\\2=2+b`

Subtract 2 from both sides to isolate b

`2-2=2+b-2\\0=b`

Therefore, the y-intercept is equal to 0. Plug this back into
`y=(1)/(3)x+b`:

`y=(1)/(3)x+0\\y=(1)/(3)x`

I hope this helps!