To determine which of the given equations has a greater slope than the line in the graph, let’s analyze the slope of the line shown and compare it with the slopes of the options provided.

Step 1: Find the Slope of the Line in the Graph

Looking at the graph, we can pick two points on the line:

• Point 1: (0, -3)
• Point 2: (3, 3)

Using the slope formula, $\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}$: $\text{slope} = \frac{{3 - (-3)}}{{3 - 0}} = \frac{6}{3} = 2$

The slope of the line in the graph is 2.

Step 2: Compare the Slopes of the Given Options

1. $y = 3x$: Slope is 3.
2. $y = \frac{4}{3}x$: Slope is $\frac{4}{3} \approx 1.33$.
3. $y = 4x$: Slope is 4.
4. $y = \frac{1}{3}x$: Slope is $\frac{1}{3} \approx 0.33$.

Step 3: Identify the Lines with Greater Slopes

We need slopes greater than 2 (the slope of the graph). From the options:

• $y = 3x$ (slope 3) and $y = 4x$ (slope 4) both have greater slopes than the graph.

Answer

The correct options are:

• $y = 3x$
• $y = 4x$

Since the question likely intends for you to choose only one answer, $y = 4x$ has the greatest slope and would be the answer.

Would you like more details or have any questions?

Related Questions

1. How do you determine the slope from a graph if the points aren't labeled?
2. Why does a steeper line on a graph represent a larger slope?
3. How would you find the slope of a line perpendicular to the given line?
4. What is the slope-intercept form of a linear equation, and how is it useful?
5. How do you calculate the slope if given an equation not in slope-intercept form?

Tip

When comparing slopes, larger absolute values indicate steeper lines, while positive and negative signs show direction (upwards vs. downwards).