Write the slope-intercept form of the equation of the line through the given two points of the line through (-2, 4) and (1, 1)

Question

I need help I have an assignment with this question due tonight and I am stuck.

Answer 1

In the comments section for this post we determined the slope of the line is -1.

To write the equation of the line containing those two points, pick one of the points, then use either point-slope or slope-intercept forms to write the equation.

First let's use point (1, 1).

Using point-slope looks like this:

y - 1 = -1(x -1)

y - 1 = -x + 1 [distribute the -1 to remove parentheses]

y = -x +2 [add 1 to both sides to isolate y--transforming to slope-intercept]

Now let's use slope-intercept to start with. Since we are using (1,1) this means when x = 1, y =1.

Slope-intercept form looks like this:

y = mx + b

where y = 1, x = 1, and m = -1.

1 = -1(1) + b

1 = -1 + b

b = 2

Since b = 2 the equation in slope-intercept form is:

y = -1x + 2

or just

y = -x + 2 (same result).

To convince you it does not matter which point you use, let's use (-2, 4).

y - 4 = -1(x - [-2])

y - 4 = -x - 2

y = -x - 2 + 4

y = -x + 2

Or when x = -2, y = 4, m = -1 (substitute into y = mx + b to find b)

4 = -1(-2) + b

4 = 2+ b

b = 2

y = -x + 2

Finally visit this Desmos graph to verify and also see some cool stuff you can do on Desmos (naming points, accessing x/y coordinates of those points).

desmos.com/calculator/hjhiyhhjyf

Select the above link, right-click and choose Go to... to visit the graph.

Answer 2

Start with two-point form

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

Combine like terms and put into slope-intercept form