Question

Line A passes through (0, -3) and (5, -1). Find the equation of Line A.

Answer 1

`y=(2)/(5)x-3`

or

`y+3=(2)/(5) (x-0)`

Explanation:

Finding the Equation of a Line Given Two Points:

• In order to find the equation of a line, we must identify point (x,y) and slope (m).
• Slope formula:
  `m=(y_2-y_1)/(x_2-x_1)`
• Point-slope formula:
  `y-y_1=m(x-x_1)`
• Slope-intercept formula:
  `y=mx+b`

We are given two points on Line A: (0,-3) and (5,-1). We can assign each integer to a variable in the slope formula (see above):

`x_1=0`

`y_1=-3`

`x_2=5`

`y_2=-1`

As we have identified point, we can now work to identify slope by substituting our points into the slope formula:

`m=(-1-(-3))/(5-0)=(2)/(5)`

Now that we have identified both point and slope for Line A, we can format these values in point-slope form. Substitute values into the formula:

`y-(-3)=(2)/(5) (x-0)=y+3=(2)/(5)x`

Solve for
`y` to achieve an answer in slope-intercept form (
`y=mx+b)`:

`y=(2)/(5) x-3`