I need help with graphing

Question

Find the equation of the line (1,4) and (3,-2) in slope intercept form and graph

Answer 1

Slope intercept form is:

y = mx + b

To find the slope of the line, we can use the slope equation, in which:

m = y2 - y1 / x2 - x1

Using (1,4) and (3,-2), we know:

m = (-2 - 4) / (3-1)

= -6 / 2 = -3

If m = -3, then we can plug in one of these points to solve for b, such that:

4 = -3(1) + b

4 = -3 + b

b = 7

To check if this is correct, we can plug in the other point:

-2 = -3(3) + 7

-2 = -9 + 7

-2 = -2

So! Using the slope intercept form, we get:

y = -3x + 7

To graph the equation, you can then just plug in numbers for x and solve for y's.

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Hope this helps!

Answer 2

Alex S. did it perfectly fine, but here's another way to find the equation.

y = mx + b is what the end result should look like. (slope-intercept form where m is the slope)

To find m, the formula is y₂ - y₁/x₂ - x₁

m = (-2 - 4) / (3 - 1)

m = -6 / 2 = -3

Now use point-slope form and convert it to slope-intercept form:

y - y₁ = m(x - x₁)

y - 4 = -3(x - 1) (plugging in known values)

y - 4 = -3x + 3 (simplifying)

y = -3x + 7 (tada! slope-intercept form)

The important thing to note here is that point-slope form only uses one of the given points, whereas the slope formula uses both points. Since point-slope form already has enough going on, I try to pick the positive point if there is one, like (1, 4), just to keep things easier. Algebra can be complex enough without mixing up signs and making it worse.

To graph, start with (0, 7) as your first point since, by definition, 7 is the y-intercept. Next go down 3 marks from the 7 and to the right 1. This leads you to (1, 4) which is one of your original given points. That means your equation checks.

Hope this explanation helps you. Good luck!