math slope intercept

Question

A line has a slope of -1/2 and passes through the point (2, 4). What is the equation the this line in slope intercept form?

Answer 1

Hey there! I can help.

Slope-intercept form is just the "fancy" way of saying y = mx +b

1. m is the slope
2. b is the y-intercept

In the problem you posted, the slope was provided: -1/2. So our equation so far is...

y = (-1/2)x + b

However...we don't have a y-intercept.

The y-intercept is the point (0, _) where the line passes through the y-axis. We were not provided that point. We were given (2, 4) instead... So we will have to find it ourselves!

Let's plug in the point (2, 4) into our working equation to get the value of b (our y-intercept)!

1. y = (-1/2)x + b, using the point (2, 4)
2. 4 = (-1/2)(2) + b
3. 4 = -1 + b
4. b = 5

Now that we have our y-intercept, we can rewrite our original equation as: y = (-1/2)x + 5