Question

compare graphs and equations
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. $y = \frac{4}{5}x + 7$

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

1. $y = -20x - 13$

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

1. $y = 2x - 3$

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

Explanation:

Problem 1: \( y = \frac{4}{5}x + 7 \)

Step1: Analyze the equation's properties

The equation \( y=\frac{4}{5}x + 7 \) is in slope - intercept form \( y = mx + b \), where the slope \( m=\frac{4}{5}\) (positive, so the line should rise from left to right) and the y - intercept \( b = 7\) (the line should cross the y - axis at \( (0,7) \)).

Step2: Analyze each graph

• Graph A: The line passes through the origin \( (0,0) \), so its y - intercept is 0, not 7. Also, the slope appears to be very small (close to 0), not \( \frac{4}{5} \).
• Graph B: The line passes through the origin, y - intercept is 0, not 7. The slope is negative (since it falls from left to right), but our slope is positive.
• Graph C: The line passes through the origin, y - intercept is 0, not 7. The slope is negative, our slope is positive.
• Graph D: The two lines (maybe a typo, but assuming it's a single line) pass through the origin, y - intercept is 0, not 7. The slope is very steep (positive), but not \( \frac{4}{5} \). Since none of the graphs have a y - intercept of 7 and the correct slope, we choose "none of the graphs".

Step1: Analyze the equation's properties

The equation \( y=-20x - 13 \) is in slope - intercept form \( y = mx + b \), where the slope \( m=-20\) (a large negative slope, so the line should fall very steeply from left to right) and the y - intercept \( b=-13\) (the line should cross the y - axis at \( (0, - 13) \)).

Step2: Analyze each graph

• Graph A: Passes through the origin, y - intercept is 0, not - 13. Slope is small (close to 0), not - 20.
• Graph B: Passes through the origin, y - intercept is 0, not - 13. Slope is negative, but not as steep as - 20.
• Graph C: Passes through the origin, y - intercept is 0, not - 13. Slope is negative, but not as steep as - 20.
• Graph D: Passes through the origin, y - intercept is 0, not - 13. Slope is positive (steep), but our slope is negative. Since none of the graphs have a y - intercept of - 13 and the correct (steep negative) slope, we choose "none of the graphs".

Step1: Analyze the equation's properties

The equation \( y = 2x-3 \) is in slope - intercept form \( y=mx + b \), where the slope \( m = 2\) (positive, line rises from left to right) and the y - intercept \( b=-3\) (line crosses y - axis at \( (0,-3) \)).

Step2: Analyze each graph

• Graph A: Passes through the origin, y - intercept is 0, not - 3. Slope is small (close to 0), not 2.
• Graph B: Passes through the origin, y - intercept is 0, not - 3. Slope is negative, our slope is positive.
• Graph C: Passes through the origin, y - intercept is 0, not - 3. Slope is negative, our slope is positive.
• Graph D: Passes through the origin, y - intercept is 0, not - 3. Slope is positive and steep, but not 2 (and y - intercept is wrong). Since none of the graphs have a y - intercept of - 3 and the correct slope, we choose "none of the graphs".

Answer:

E. none of the graphs

Problem 2: \( y=-20x - 13 \)