Question

Write the equation of the line that passes through the points

(-2, -1) and (2, 4). Put your answer in fully reduced point-
slope form, unless it is a vertical or horizontal line.

Answer 1

Explanation:

Step 1 : Find the slope/gradient (this is known as "m")

The slope formula is :

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

*Note that we are given 2 points:

For the first point (-2,-1) , this means x1 = -2 and y1 = -1

For the second point (2,4), this means x2 = 2 and y2 = 4

If we substitute those values into the slope formula you end up with this:

`m = (y2-y2)/(x2-x1) = (4 - (-1))/(2 - (-2)) = (4+1)/(2+2) =(5)/(4)`

Step 2: Substitute the values into the point-slope formula:

`y - y1 = m(x- x1)`

Now that we know m = 5/4 , you can substitute this into the above formula and you get:

`y - y1 = m(x- x1)`

`y - (-1) = (5)/(4) (x - (-2)) \\y + 1 = (5)/(4) ( x + 2)`

`y = (5)/(4)(x + 2) - 1`