Question

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Answer 1

Answer: the x-intercept is (-10,0), the y-intercept is (0,45/2)

Explanation:

First, we need to determine the function describing the line.

From the table, it is obvious that the y values increase by 9 every increase of 4 of the x values. So, the slope is 9/4 and the function looks like this:

$y = m x+ b = \frac{9}{4}x + b$

with the y-intercept (or bias) b still unknown. This can be determined by using one of the point from the table, like so:

$-18 = \frac{9}{4}\cdot 2+b\\\implies b = -18 -\frac{9}{2}=\frac{45}{2}\\y = \frac{9}{4}x+\frac{45}{2}$

The above function form makes it easy to read off the y-intercept, which is (0,45/2) or (0,22.5). The x-intercept is obtained by setting y = 0 and solving for x:

$y = \frac{9}{4}x+\frac{45}{2}\\0 = \frac{9}{4}x+\frac{45}{2}\\-\frac{45}{2}=\frac{9}{4}x\\x = -10$

The x-intercept is (-10,0)

Answer 2

Answer:

y-intercept = (0,-27/2); x-intercept = (-6,0)

Explanation:

The equation for a straight line is

y = mx + b

Step 1. Calculate the slope

m = (y₂ - y₁)/(x₂ - x₁)

y₂ = - 36; y₁ = -18

x₂ = 10; x₁ = 2

m = [- 36 – (-18)]/(10-2)

m = (-36 + 18)/8

m = -18/8

m = -9/4

===== ==========

Step 2. Calculate the y-intercept

y = -(9/4)x + b

When x = 2, y = -18      Insert the values

        -18 = -(9/4)×2 + b

        -18 = -9/2 +b

-18 + 9/2 = b

            b = (-36 + 9)/2

           b = -27/2

The y-intercept is at (0, -27/2).

===== ==========

Step 3. Calculate the x-intercept

y = -(9/4)x – 27/2      Set y = 0

0 = -(9/4)x – 27/2     Multiply each side by -1

0 = (9/4)x + 27/2      Multiply each side by 4

0 = 9x + 54               Divide each side by 9

0 = x + 6                    Subtract 6 from each side

x = -6

The x-intercept is at (-6, 0).

The graph shows the x-intercept at (-6,0) and the y-intercept at (0, -27/2).