Answer:
[tex]m = -\frac{2}{5}[/tex] ---- slope
[tex]y = -\frac{1}{3}[/tex] --- y intercept
Step-by-step explanation:
Given
The attached table
Required
Calculate the slope and y intercept
First, we need to calculate the slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From the table, the following relationships exist:
[tex](x_1,y_1) = (-\frac{3}{4},-\frac{1}{30})[/tex]
[tex](x_2,y_2) = (\frac{1}{4},-\frac{13}{30})[/tex]
So, the expression for calculating slope becomes:
[tex]m = [-\frac{13}{30} - (-\frac{1}{30})] / [\frac{1}{4} - (-\frac{3}{4})][/tex]
[tex]m = [-\frac{13}{30} +\frac{1}{30}] / [\frac{1}{4} +\frac{3}{4}][/tex]
Take LCM
[tex]m = [\frac{-13+1}{30}] / [\frac{1+3}{4}][/tex]
[tex]m = [\frac{-12}{30}] / [\frac{4}{4}][/tex]
[tex]m = [\frac{-12}{30}] / 1[/tex]
[tex]m = \frac{-12}{30}[/tex]
[tex]m = \frac{-2}{5}[/tex]
[tex]m = -\frac{2}{5}[/tex]
To calculate the y intercept:
x must be 0. i.e.
[tex]x = 0[/tex]
So, we have:
[tex](x_1,y_1) = (-\frac{3}{4},-\frac{1}{30})[/tex]
[tex](x_2,y_2) = (0,y)[/tex]
[tex]m = -\frac{2}{5}[/tex]
Substitute these values in:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{2}{5} = [y - (-\frac{1}{30})] / [0- (-\frac{3}{4})][/tex]
[tex]-\frac{2}{5} = [y +\frac{1}{30}] / [0+\frac{3}{4}][/tex]
[tex]-\frac{2}{5} = [y +\frac{1}{30}] / [\frac{3}{4}][/tex]
Multiply through by 3/4
[tex]-\frac{2}{5}*\frac{3}{4} = y +\frac{1}{30}[/tex]
[tex]-\frac{6}{20} = y +\frac{1}{30}[/tex]
[tex]-\frac{3}{10} = y +\frac{1}{30}[/tex]
Collect Like Terms
[tex]y = -\frac{3}{10}-\frac{1}{30}[/tex]
[tex]y = \frac{-9-1}{30}[/tex]
[tex]y = \frac{-10}{30}[/tex]
[tex]y = \frac{-1}{3}[/tex]
[tex]y = -\frac{1}{3}[/tex]
