Question

What are the slope and the y-intercept of the linear function that is represented by the table? x y –1 Negative three-halves Negative one-half 0 0 Three-halves One-half 3 The slope is –3, and the y-intercept is Negative one-half. The slope is –3, and the y-intercept is Three-halves. The slope is 3, and the y-intercept is Negative one-half. The slope is 3, and the y-intercept is Three-halves.

Answer 1

Answer:

The slope of the line is 3 and the y-intercept is (3/2) three-halves.

Step-by-step explanation:

The data provided is:

 X     Y

-1.0     -1.5

-0.5     0.0

0.0     1.5

0.5     3.0

The slope of the linear function is denoted by, b and the intercept is denoted by, a.

The formula to compute the slope and intercept are:

$a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}$

Compute the values required in Excel.

Compute the slope and intercept as follows:

$a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 3 \cdot 1.5 - (-1) \cdot 3}{ 4 \cdot 1.5 - (-1)^2} \approx \frac{3}{2} \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 4 \cdot 3 - (-1) \cdot 3 }{ 4 \cdot 1.5 - \left( -1 \right)^2} \approx 3\end{aligned}$

Thus, the slope of the line is 3 and the y-intercept is (3/2) three-halves.

Answer 2

Answer:

The slope is 4, and the y-intercept is Negative five-halves.

Step-by-step explanation: