1) Slope is defined as the rise over the run.
In essence, the slope becomes -2 (A)
2) Use the formula: [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]\frac{1 + 3}{1 + 2} = \frac{4}{3}[/tex] (D)
3) Constant variation is defined as: y = kx, where k is the constant variation.
Thus, divide both sides by -4, to find that k = -2 (B)
4) The constant variation is defined as y/x, plugging in the values yields: a constant of 3.
Now, y = 3x is our equation.
Thus, when x = 10, y = 30
5) y-intercept at 9 indicates this: (0, 9)
Using point-gradient form, we produce:
[tex]y - 9 = \frac{2}{3}(x - 0)[/tex]
[tex]y = \frac{2}{3}x + 9[/tex] (C)
6) Find the gradient using the two point-gradient form:
[tex]\frac{1 + 3}{3 - 1} = 2[/tex]
Substituting one of the points will yield:
[tex]y - 1 = 2(x - 3)[/tex]
[tex]y - 1 = 2x - 6[/tex]
[tex]y = 2x - 5[/tex] (D)
