Question

1. match each equation with its possible graph shown below. (1 point each)

a. y = 4
b. y = 1/2x - 6
c. y = -1/2x + 10
d. y = -3x - 10
(i) (ii) (iii)
(iv) (v) (vi)

Explanation:

Step1: Analyze equation a

The equation $y = 4$ is a horizontal line. It has a $y$-intercept of 4 and a slope of 0. So it matches graph (i).

Step2: Analyze equation b

The equation $y=\frac{1}{2}x - 6$ is in slope - intercept form $y=mx + b$ where $m=\frac{1}{2}$ (positive slope) and $b=-6$ (negative $y$-intercept). So it matches graph (iv) which has a positive slope and a negative $y$-intercept.

Step3: Analyze equation c

The equation $y =-\frac{1}{2}x+10$ has a negative slope ($m =-\frac{1}{2}$) and a positive $y$-intercept ($b = 10$). So it matches graph (v) which has a negative slope and a positive $y$-intercept.

Step4: Analyze equation d

The equation $y=-3x - 10$ has a negative slope ($m=-3$) and a negative $y$-intercept ($b=-10$). So it matches graph (vi) which has a steep negative slope and a negative $y$-intercept.

Answer:

a. (i)
b. (iv)
c. (v)
d. (vi)