Question

Which equation represents the line that passes through points (1, –5) and (3, –17)?

Answer 1

`y=-6x+1`

Explanation:

The linear equation with slope m and intercept c is given as follows:

`y=mx+c`

The formula for slope of line with points
`(x_(1) ,y_(2) )` and
`(x_(2) ,y_(2) )` can be expressed as,

`m=(y_(2) -y_(1) )/(x_(2) -x_(1) )`

The line passes the points that are
`(1,-5)` and
`(3,-17)`

The slope of the line can be obtained as follows:

`m=(-17-(-5))/((3)-1)`

`m=(-12)/(2)`

`m=-6`

The slope of the line is
`-6`

The line passes through the point
`(3,-17)`

Substitute 3 for x, - 6 for m and -17 for y in equation
`y=mx+c` to obtain the value of c.

`-17=-6(3)+c`

`-17=-18+c`

`-17+18=c`

`1=c`

The equation is
`y=-6x+1`

Hence, the equation of the line that passes through the points
`(1,-5)` and
`(3,-17)` is
`y=-6x+1`

Answer 2

y = -6x + 1

Explanation:

y = mx + b

b = slope = (-5 - (-17))/(1 - 3) = 12/(-2) = -6

y = -6x + b

-5 = -6(1) + b

b = 1

y = -6x + 1