Question

Which represents the equation of the line that
passes through the points (5,-2) and (15, 6)?

Answer 1

`y =(4)/(5)x-6`

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 given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (5,-2) and (15, 6)

`=(6-(-2))/(15-5)\\=(6+2)/(15-5)\\=(8)/(10)\\=(4)/(5)`

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

`y =(4)/(5)x+b`

2) Determine the y-intercept (b)

`y =(4)/(5)x+b`

Plug in one of the given points and solve for b

`6=(4)/(5)(15)+b\\6=12+b`

Subtract 12 from both sides of the equation to isolate b

`6-12=12+b-12\\-6=b`

Therefore, the y-intercept of the line is -6. Plug this back into
`y =(4)/(5)x+b`:

`y =(4)/(5)x-6`

I hope this helps!