A graph with a coordinate plane.

Question

The x-axis and y-axis are labeled, and both extend from -10 to 10. 

There are two lines: a red line and a light-teal/turquoise line. The red line is a straight line sloping downward from left to right. The teal line is also a straight line forming a rectangle with the red line to the right of the origin.

There are three vertices on the graph with the coordinates of A, B, and C in an orange rectangle. The light teal line has vertices D, E, G, and F.

What is the slope of the graph?
What is b if the y-intercept is (0, b) ?
We would shift the graph up ____ units to make this proportional.
The slope triangles show that ___/9 = 4/3 .
The option "4" (6 of 14) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

options for response areas:
0
-4
8
-10
-5
4
5
-8
12
4/3
3/4
-4/3
-5/10
5/10

Answer 1

To find the slope of the red line and the y-intercept (b), we need some additional information; however, I can guide you through a general approach based on the scenario you've described.

1. Slope of the Graph: The slope (m) of a line is calculated as the change in y divided by the change in x, often referred to as rise/run. If you have two points on the red line, (x1, y1) and (x2, y2), then the slope is calculated as: \[ m = \frac{y2 - y1}{x2 - x1} \]

2. Y-Intercept (b): The y-intercept (b) is the point where the line crosses the y-axis, which occurs at x = 0. By substituting x = 0 into the equation of the line (if you have it in slope-intercept form, y = mx + b), you can directly identify the value of b.

3. Shifting the Graph: To make a graph proportional (to ensure the same slope), you may need to shift it vertically. The number of units to shift would depend on your desired proportionality or the context provided.

4. Slope Triangles: If you see that the slopes are represented by triangles (right triangles in the coordinate plane), then the formula you mention, \( \frac{\text{rise}}{\text{run}} = \frac{4}{3} \), suggests a relationship between vertical and horizontal distances. If one leg of the triangle (rise) represents some vertical change, and the other leg (run) represents a horizontal change, the actual values would depend on the specific coordinates.

Without specific values for the vertices A, B, C, D, E, G, and F or exact locations for measuring slopes and intercepts, I recommend substituting values based on your graph to determine answers to each of the inquiries.

If you have additional information (like coordinates or key points), I can provide a more detailed solution!