Answer:
[tex]x = -1[/tex]
[tex]y = 3[/tex]
Step-by-step explanation:
Given
The attached table
Required
Fill in the blanks
First, we need to calculate the slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Where:
[tex](x_1,y_1) = (1/2,1)[/tex]
[tex](x_2,y_2) = (3,-9)[/tex]
So, we have:
[tex]m = \frac{-9-1}{3-1/2}[/tex]
[tex]m = \frac{-10}{3-0.5}[/tex]
[tex]m = \frac{-10}{2.5}[/tex]
[tex]m = -4[/tex]
Next, we calculate the equation:
[tex]y - y_2 = m(x - x_2)[/tex]
This gives:
[tex]y - (-9) = -4(x - 3)[/tex]
[tex]y +9 = -4(x - 3)[/tex]
[tex]y +9 = -4x +12[/tex]
Make y the subject:
[tex]y = -4x +12-9[/tex]
[tex]y = -4x +3[/tex]
So,
When y = 7:
We have:
[tex]y = -4x +3[/tex]
[tex]7 = -4x +3[/tex]
Collect Like Terms
[tex]4x = 3 - 7[/tex]
[tex]4x = -4[/tex]
Divide through by 4
[tex]x = -1[/tex]
When x = 0, we have:
[tex]y = -4x +3[/tex]
[tex]y = -4 * 0 + 3[/tex]
[tex]y = 0 + 3[/tex]
[tex]y = 3[/tex]
