Which equation represents the graph given below? Select one: a. 5y – 2x = -1 b. 3y + 2x = 1 c. 5y + 2x = -1 d. 2x – 5y = -1 How should you graph the equation y = 8x – 7 using the slope-intercept form? Select one: a. Plot a point at 7 on the y-intercept. Then travel up 8 units and to the right 1 unit and plot another point. Connect the points to create a line. b. Plot a point at -7 on the x-intercept. Then travel up 1 unit and to the right 8 units and plot another point. Connect the points to create a line. c. Plot a point at 8 on the y-intercept. Then travel down 7 units and to the right 1 unit and plot another point. Connect the points to create a line
The Correct Answer and Explanation is:
Correct Answers:
First question: c. 5y + 2x = -1
Second question: a. Plot a point at -7 on the y-intercept. Then travel up 8 units and to the right 1 unit and plot another point. Connect the points to create a line.
Explanation
Finding the Equation from the Graph
To determine which equation represents the graphed line, we first need to find the line’s slope (m) and y-intercept (b). We can find the slope by identifying two distinct points on the line and using the formula m = (y2 – y1) / (x2 – x1).
By examining the graph, we can clearly identify two points where the line crosses the grid intersections: (-3, 1) and (2, -1).
Using these points, we calculate the slope:
m = (-1 – 1) / (2 – (-3)) = -2 / (2 + 3) = -2/5.
Now that we have the slope (m = -2/5), we can use one of the points (let’s use (2, -1)) and the slope-intercept form (y = mx + b) to find the y-intercept (b).
-1 = (-2/5)(2) + b
-1 = -4/5 + b
b = -1 + 4/5 = -1/5.
The equation of the line is y = (-2/5)x – 1/5. To match this with the given options, we convert it to standard form. First, multiply the entire equation by 5 to eliminate the fractions:
5y = -2x – 1
Then, add 2x to both sides:
2x + 5y = -1. This matches option c. 5y + 2x = -1.
Graphing Using Slope-Intercept Form
The second question asks how to graph the equation y = 8x – 7. This equation is already in the slope-intercept form, y = mx + b.
Here, the slope (m) is 8, and the y-intercept (b) is -7.
The process to graph this is as follows:
- Plot the y-intercept: The y-intercept is the point where the line crosses the y-axis. In this case, b = -7, so our first point is at (0, -7).
- Use the slope to find a second point: The slope, m = 8, can be written as a fraction, 8/1. This represents the “rise over run”. From the y-intercept point (0, -7), we “rise” 8 units (move up 8 units) and “run” 1 unit (move to the right 1 unit). This brings us to a second point at (1, 1).
- Draw the line: Connect the two points, (0, -7) and (1, 1), with a straight line.
This procedure is described perfectly in option a.thumb_upthumb_down
