Question

Write the equation of a line that passes through the points ( 2 , - 5 ) and ( 8 , - 2 )

Answer 1

`y=(1)/(2)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 points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (2,-5) and (8,-2)

`m=(y_2-y_1)/(x_2-x_1)\\=(-2-(-5))/(8-2)\\=(-2+5)/(8-2)\\=(3)/(6)\\=(1)/(2)`

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

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

2) Determine the y-intercept (b)

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

Plug in one of the given points and solve for b

`-5=(1)/(2)(2)+b\\-5=1+b`

Subtract 1 from both sides to isolate b

`-5-1=1+b-1\\-6=b`

Therefore, the y-intercept of the line is -6. Plug this back into
`y=(1)/(2)x+b`:

`y=(1)/(2)x+(-6)\\y=(1)/(2)x-6`

I hope this helps!