Question

A linear function contains the following points,
What are the slope and y-intercept of this function

A. The slope is 3/4
The y-intercept is (0, -2).
B. The slope is 3.
The y-intercept is (0, -2).
C. The slope is 4/3
The y-intercept is (0, -2).
D. The slope is 3/4
The y-intercept is (-2,0).

Answer 1

The slope and the y-intercept of the linear function containing the points given in the table are:

A. The slope is 3/4

The y-intercept is (0, -2)

Recall:

• Slope-intercept form is: y = mx + b, where, y-intercept = b, and m = slope

Given the pairs of points on the table as (0, -2) and (4, 1), we can find the slope and the y-intercept as follows:

Slope of the line = rise/run = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{0 - 4} = \frac{-3}{-4} = \frac{3}{4}$

slope (m) = 3/4

To find the y-intercept (b), substitute (x, y) = (4, 1) and m = 3/4 into y = mx + b

• Thus:

$1 = \frac{3}{4} (4) + b\\\\1 = 3 + b\\\\1 - 3 = b\\\\-2 = b\\\\b = -2$

This means, the value of y when x is 0 is: -2 (0, -2).

Therefore the slope and the y-intercept of the linear function containing the points given in the table are:

A. The slope is 3/4

The y-intercept is (0, -2)

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