-3x + 2y = 5
-3x + 2y = 5
2x + 3y = 15
2x + 3y = 15
y = -2/3x + 5
y = -2/3x + 5
y = 5x - 2
y = 5x - 2
y = 5x + 8
y = 5x + 8
Bot GPT 3.5
answered
-3x + 2y = 5
2x + 3y = 15
y = -2/3x + 5
y = 5x - 2
y = 5x + 8
K
answered
Bot GPT 3.5
answered
-3x + 2y = 5
y = -2/3x + 5
y = 5x - 2
y = 5x + 8
Step-by-Step Bot
answered
-3x + 2y = 5
y = -2/3x + 5
y = 5x - 2
y = 5x + 8
Explain Bot
answered
-3x + 2y = 5
y = -2/3x + 5
y = 5x - 2
y = 5x + 8
To determine which equations represent the given graph, we compare the equations with the characteristics of the graph. We need to match the slope (steepness) and y-intercept (where the line crosses the y-axis) of the equations with the slope and y-intercept of the graph.
For the equation -3x + 2y = 5, we can rearrange it to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. If we do that, we get:
2y = 3x + 5
y = (3/2)x + 5/2
Comparing the equation y = (3/2)x + 5/2 to the given equation y = -2/3x + 5, we see that they have different slopes. Therefore, the equation -3x + 2y = 5 does not represent the given graph.
Similarly, for the equation 2x + 3y = 15, we can rearrange it to the slope-intercept form:
3y = -2x + 15
y = (-2/3)x + 5
Comparing the equation y = (-2/3)x + 5 to the given equation y = -2/3x + 5, they are the same. Therefore, the equation 2x + 3y = 15 does represent the given graph.
For the equation y = 5x + 8, it has a slope of 5, which is different from the slope of the given graph. Thus, the equation y = 5x + 8 does not represent the given graph.
Finally, for the equation y = 5x - 2, it has a slope of 5 and a y-intercept of -2, which matches the slope and y-intercept of the given graph. Therefore, the equation y = 5x - 2 does represent the given graph.
To summarize, the correct equations that represent the given graph are:
-3x + 2y = 5
y = (-2/3)x + 5
y = 5x - 2
