Question

Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.

Question:

What was Brooke’s error?

•She found the incorrect slope in step 1.
•She mixed up the x- and y-coordinates when she plugged in the point in step 2.
•She found the incorrect y-intercept in step 2.
•She mixed up the slope and y-intercept when she wrote the equation in step 3.

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

`m = \frac {y2-y1} {x2-x1}`

We have the following points:

`(x1, y1): (- 7,25)\\(x2, y2): (- 4,13)`

Substituting the values:
`m = \frac {13-25} {- 4 - (- 7)} = \frac {-12} {- 4 + 7} = \frac {-12} {3} = - 4`

Thus, the line is of the form:

`y = -4x + b`

We substitute one of the points and find "b":

`13 = -4 (-4) + b\\13 = 16 + b\\b = 13-16 = -3`

Finally we have to:

`y = -4x-3`

Answer:

The equation es
`y = -4x-3`

Answer 2

She mixed up the slope and y-intercept when she wrote the equation in step 3.