Question

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

Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4


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

Brooke's error was that she found the incorrect slope in step 1.

The slope formula is: m = (y₂ - y₁) / (x₂ - x₁)

Using the given points: m = (13 - 25) / (-4 - (-7)) m = -12 / 3 m = -4

So, the slope is -4, not -12/3 as Brooke calculated in step 1.

The correct equation for the line passing through the points (-7, 25) and (-4, 13) is: y = -4x - 3 (as found in step 3)

Answer 2

she mixed up the slope and y- intercept in step 3

Explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

she correctly calculated the slope as m = - 4 and the y- intercept b = - 3

thus equation she should have is

y = - 4x - 3