Question

What is the slope-intercept form of a line?  What two specific pieces of information do you need to write an equation of a line in slope-intercept form?  Explain/discuss how you would find those two pieces of information if you were only given two points on the line.  Use the points (-3,1) and (3,-5) to illustrate this process.

Answer 1

The slope-intercept form of a line is:

y = ax + b

In which a is the slope and b is the y-intercept, which is the value of y when x = 0.

To write an equation in this form, we need the slope and the y-intercept.

Using two points, we find the slope a dividing the change in y by the change in x. Then, having a, we can replace one of these points into the equation, to find the intercept b.

In this question:

We have points (-3,1) and (3,-5)

Finding the slope:

Change in y: -5 - 1 = -6

Change in x: 3 - (-3) = 3 + 3 = 6

Slope: a = -6/6 = -1

So

y = -x + b

Using the point (-3,1), we have that when x = -3, y = 1. So

1 = -(-3) + b

1 = 3 + b

3 + b = 1

b = 1 - 3

b = -2

The equation is:

y = -x - 2