Question

A student was trying to use the points (1, -19) and (-2, -7) to write an equation of a line in slope-intercept form.

Find and explain the error in the work below.
-7-(-19) 12
-2-1
y = mx + b
1 = -4(-19) + b
1-
76+ b
-76 <-76
-75 = b
Equation: y
-
<=-4
75

Answer 1

The student made an error in computing the slope and y-intercept. The correct slope is -4 and the correct y-intercept is -15, leading to the equation of the line y = -4x - 15.

Step-by-step explanation:

The student has made an error in calculating the slope of the line passing through the points (1, -19) and (-2, -7).

The slope (m) should be calculated using the formula m = (y2 - y1) / (x2 - x1).

Therefore, the correct slope is m = (-7 - (-19)) / (-2 - 1) = 12 / -3 = -4.

Next, to find the y-intercept (b), we could use one of the points and the slope in the formula y = mx + b.

By plugging the coordinates of the point (1, -19) into the equation,

we get -19 = -4(1) + b, which simplifies to b = -15.

Therefore, the correct equation of the line in slope-intercept form is y = -4x - 15.