Question
graph the linear equation y = 3x + 2
(use the illustrations in the answers described to pick the correct graph described)
1. A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis negative 2 comma 2 right parenthesis, and left parenthesis 0 comma 1 right parenthesis.
2. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
3. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. he line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis. A dotted vertical line labeled 3 from left parenthesis 1 comma negative 5 right parenthesis and a dotted horizontal line labeled 1 from left parenthesis 0 comma negative 2 right parenthesis intersect at left parenthesis 1 comma negative 2 right parenthesis, forming a right triangle with the slope.
4. A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 2 right parenthesis, and left parenthesis 1 comma negative 1 right parenthesis.
(use the illustrations in the answers described to pick the correct graph described)
1. A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis negative 2 comma 2 right parenthesis, and left parenthesis 0 comma 1 right parenthesis.
2. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
3. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. he line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma negative 5 right parenthesis. A dotted vertical line labeled 3 from left parenthesis 1 comma negative 5 right parenthesis and a dotted horizontal line labeled 1 from left parenthesis 0 comma negative 2 right parenthesis intersect at left parenthesis 1 comma negative 2 right parenthesis, forming a right triangle with the slope.
4. A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 2 right parenthesis, and left parenthesis 1 comma negative 1 right parenthesis.
Answers
GPT-4o mini
To determine which graph corresponds to the linear equation \(y = 3x + 2\), we can analyze the slope and y-intercept of the equation.
1. The slope (m) is 3, which means for every unit increase in x, y increases by 3. The y-intercept (b) is 2, meaning the line crosses the y-axis at (0, 2).
Now let's review the options:
1. The first graph shows two points (−2, 2) and (0, 1), but it does not have the correct y-intercept (it should be (0, 2), not (0, 1)).
2. The second graph shows the line passing through points (0, 3) and (1, 5). The y-intercept is 3, which does not match with our expected intercept of 2.
3. The third graph shows a downward sloping line with points (0, -2) and (1, -5). This does not match the positive slope of our equation.
4. The fourth graph shows points (0, 2) and (1, -1). The point (0, 2) is the correct y-intercept, but the point (1, -1) does not correspond with the slope of 3.
None of the options match perfectly with the equation \(y = 3x + 2\) based solely on the provided points. The best evidence is the need for a line that passes through (0, 2) and has a steep slope, indicative of \(y\) values increasing by 3 for every increase of 1 in \(x\).
Given the plotted points, if the option had a line that went through (0, 2) and (1, 5) as indicated in option 2, it would represent the equation correctly, with the slope being 3, but that is incorrect based on the total description mapping.
From your options, none directly give the exact line related to the stated property, but option 2 is the closest which meets the criteria for a slope of 3.
1. The slope (m) is 3, which means for every unit increase in x, y increases by 3. The y-intercept (b) is 2, meaning the line crosses the y-axis at (0, 2).
Now let's review the options:
1. The first graph shows two points (−2, 2) and (0, 1), but it does not have the correct y-intercept (it should be (0, 2), not (0, 1)).
2. The second graph shows the line passing through points (0, 3) and (1, 5). The y-intercept is 3, which does not match with our expected intercept of 2.
3. The third graph shows a downward sloping line with points (0, -2) and (1, -5). This does not match the positive slope of our equation.
4. The fourth graph shows points (0, 2) and (1, -1). The point (0, 2) is the correct y-intercept, but the point (1, -1) does not correspond with the slope of 3.
None of the options match perfectly with the equation \(y = 3x + 2\) based solely on the provided points. The best evidence is the need for a line that passes through (0, 2) and has a steep slope, indicative of \(y\) values increasing by 3 for every increase of 1 in \(x\).
Given the plotted points, if the option had a line that went through (0, 2) and (1, 5) as indicated in option 2, it would represent the equation correctly, with the slope being 3, but that is incorrect based on the total description mapping.
From your options, none directly give the exact line related to the stated property, but option 2 is the closest which meets the criteria for a slope of 3.