Question

determine which graphs, if any, can represent each equation. select all that apply. select none of the graphs if none represent the equation. if more information is needed, select not enough information.
graph a
graph b
graph c
graph d
circle your choice(s):
explain your choice(s):

1. $y = -\frac{6}{5}x - 4$

a. graph a c. graph c
b. graph b d. graph d
e. none of the graphs
f. not enough information

1. $y = 5x + 1$

a. graph a c. graph c
b. graph b d. graph d
e. none of the graphs
f. not enough information

1. $y = -\frac{1}{3}x + 2$

a. graph a c. graph c
b. graph b d. graph d
e. none of the graphs
f. not enough information

Explanation:

Question 4:

Step1: Analyze the slope and y-intercept

The equation is \( y = -\frac{6}{5}x - 4 \). The slope \( m = -\frac{6}{5} \) (negative, moderate steepness) and y-intercept \( b = -4 \) (below the origin).

Step2: Check the graphs

• Graph A: Passes through origin (\( b = 0 \)), not matching \( b = -4 \).
• Graph B: Negative slope, steep (slope magnitude large), but let's check y-intercept. The graph passes through origin? No, wait, the equation has \( b = -4 \), but all given graphs pass through origin (0,0)? Wait, no, looking at the graphs: all graphs (A, B, C, D) pass through the origin (0,0). But our equation has \( y \)-intercept \( -4 \), so none of the graphs have \( y \)-intercept \( -4 \) (they all pass through (0,0)). Also, slope: \( -\frac{6}{5} \) is -1.2, Graph B has a steep negative slope (maybe more negative than -1.2? But even if slope matches, y-intercept doesn't. So none of the graphs represent \( y = -\frac{6}{5}x - 4 \) because they all pass through (0,0) (y-intercept 0) while the equation has y-intercept -4.

Step1: Analyze the slope and y-intercept

The equation is \( y = 5x + 1 \). Slope \( m = 5 \) (positive, steep) and y-intercept \( b = 1 \) (above origin).

Step2: Check the graphs

• Graph A: Shallow positive slope, not steep.
• Graph B: Negative slope, no.
• Graph C: Negative slope, no.
• Graph D: Positive, steep slope. But check y-intercept: Graph D passes through origin? Wait, the graph D: does it pass through (0,1)? No, it passes through origin (0,0). But our equation has \( b = 1 \), so y-intercept is 1, but Graph D passes through (0,0). Wait, maybe the graphs are drawn with origin, but the equation has \( b = 1 \). However, among the graphs, Graph D has a steep positive slope (matches \( m = 5 \) steepness). But y-intercept: the equation has \( b = 1 \), but the graph D passes through (0,0). Wait, maybe the graphs are simplified, but let's check slope. \( m = 5 \) is very steep, positive. Graph D has a steep positive slope. So among the options, Graph D is the only one with steep positive slope. But wait, y-intercept: the equation has \( b = 1 \), but Graph D passes through (0,0). Hmm, maybe the graphs are drawn without showing the exact y-intercept, but focusing on slope. So Graph D has a steep positive slope, matching \( m = 5 \).

Step1: Analyze the slope and y-intercept

The equation is \( y = -\frac{1}{3}x + 2 \). Slope \( m = -\frac{1}{3} \) (negative, shallow) and y-intercept \( b = 2 \) (above origin).

Step2: Check the graphs

• Graph A: Shallow positive slope, no.
• Graph B: Steep negative slope, no.
• Graph C: Negative slope, shallow? Wait, Graph C: let's see, slope of Graph C: if it's a line through origin, slope is \( \frac{y}{x} \). The line goes from top left to bottom right, shallow? Wait, \( -\frac{1}{3} \) is a shallow negative slope (slope of -1/3). Graph C: let's check slope. If the line is \( y = -x \) (slope -1), which is steeper than -1/3. Wait, no: \( -\frac{1}{3} \) is less steep (closer to horizontal) than -1. So Graph C has slope -1 (steeper), Graph A has shallow positive, Graph B steep negative, Graph D steep positive. So none of the graphs have a shallow negative slope (\( -\frac{1}{3} \)) and y-intercept 2 (all graphs pass through origin, y-intercept 0). So none of the graphs represent this equation.

Answer:

E. none of the graphs

Question 5: