Explanation:
To determine which equation represents the line shown in the graph, you'll need to compare the equation's slope (m) and y-intercept (b) with the characteristics of the graph. The equation for a line in slope-intercept form is y = mx + b, where:
- "m" is the slope (the coefficient of x).
- "b" is the y-intercept (the constant term).
The given equations are:
1. y = (2/5)x - 1
2. y = (5/2)x - 1
3. y = (5/2)x + 1
4. y = (2/5)x + 1
Now, let's compare each equation with the characteristics of the graph:
- The slope of the line in the graph represents how steep it is.
- The y-intercept is the point where the line crosses the y-axis (where x = 0).
Given the graph, let's analyze the characteristics:
- If the line is steep and crosses the y-axis below the origin, the slope should be positive, and the y-intercept should be negative.
- If the line is steep and crosses the y-axis above the origin, the slope should be positive, and the y-intercept should be positive.
Looking at the equations:
1. y = (2/5)x - 1: This equation has a positive slope and a negative y-intercept. It's a possibility.
2. y = (5/2)x - 1: This equation has a positive slope and a negative y-intercept. It's also a possibility.
3. y = (5/2)x + 1: This equation has a positive slope and a positive y-intercept. It does not match the graph's characteristics.
4. y = (2/5)x + 1: This equation has a positive slope and a positive y-intercept. It also does not match the graph's characteristics.
So, based on the characteristics of the graph, equations 1 and 2 are potential matches. To determine the correct equation, you may need additional information or context about the specific graph or problem you are working on.