Question

Determine the slope and y-intercept of a line that passes through the points (-2, 6) and

(4, -3).

Answer 1

Y = 3

Explanation:

Y = -3/2x +3

Y = -3/2 × 0 + 3

Y = 3

Answer 2

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

Explanation:

Step 1 - Calculate slope first via the equation:

`(y2 - y1)/(x2 - x1)`

Where x1 and y1 are the coordinates of the first set whereas x2 and y2 are the second set. Plug the variables in:

`(6 - (-3))/(-2 - 4) \\(6 + 3 ))/(-2 - 4) \\(9)/(-6)`

Which simplifies to:

`(3)/(-2)`

Now, in the line equation form we know x:

y = mx + c

y =
`(3)/(-2)`x + c

Step 2 - Calculate y intercept

Plug the variables of one point into the above equation:

y =
`(3)/(-2)`x + c

`6 = (3)/(-2)(-2) + c`

`6 = (3)/(-2)(-2) + c \\6 = 3 + c\\6 - 3 = c\\c = 3\\`

Meaning that the full line equation is:

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

Hope this helps!