Question

Which is the correct slope-intercept equation for a line that passes through the points (1,-3) and (-3,17)

Answer 1

`y=-5x+2`

Explanation:

Hi there!

What we need to know:

• Slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

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

Plug in the given points (1,-3) and (-3,17)

`=(17-(-3))/(-3-1)\\=(17+3)/(-3-1)\\=(20)/(-4)\\=-5`

Therefore the slope of the line is -5. Plug this into
`y=mx+b`:

`y=-5x+b`

2) Determine the y-intercept (b)

`y=-5x+b`

Plug in one of the given points and solve for b

`-3=-5(1)+b\\-3=-5+b`

Add 5 to both sides of the equation to isolate b

`-3+5=-5+b+5\\2=b`

Therefore, the y-intercept of the equation is 2. Plug this back into
`y=-5x+b`:

`y=-5x+2`

I hope this helps!