Find the equation of a line that passes through the points (-1,5) and (3,-3). Write the equation in slope-intercept, point-slope, and standard form.

Answer 1

First step is to solve for the slope. That is the change in Y / change in X, in this case (5+3)/(-1-3) or -2.

With the slope, and a point you have the point-slope form. The formula is Y2-Y1= m(X2-X1)

I'll use the point (-1,5), and m is -2. That means you have Y-5= -2(X+1)

You get slope-intercept form by solving that equation for Y. First distribute the -2, for Y-5= -2X-2. Then add 5 to both sides for Y= -2X+3

Standard form is written as Ax+By=C so you need to have X and Y on the same side of the equation. You can get this by adding 2X to both sides for 2X+Y=3

Answer 2

The first thing we should always do for these problems is find the slope of the line:

slope = m = y₂ - y₁ = -3 - 5 = -8 = -2

x_{2 -} x₁ 3 - (-1) 4

Now we can go about solving for the y-intercept. The easiest way for me to find it is using slope-intercept form:

y = (m)(x) + b , b= y-intercept

b = y - (m)(x) , Now we plug in the slope we just found and a set of points

b = 5 - (-2)(-1) = 2

This then makes the slope-intercept equation y = -2x + 2

Standard form of a line is in the form of Ax + By = C, so we move the x and y components to the same side.

2x + y = 2

Point-slope form is similar to slope intercept form point but incorporates a point rather than the y-intercept. The general form is (y - y₁) = m (x - x₁). Plugging in either point we are given, we get:

(y - 5) = -2 (x + 1)

In Summary:

Slope-Intercept - y = -2x + 2

Standard Form - 2x + y = 2

Point-Slope Form- (y - 5) = -2 (x + 1)

Answer 3

The slope is (5+3/(-1-3) = -2

The point slope form is -2 = (y+3)(x-3).

You can "massage" this form around into the form needed!