Graph the linear equation y=2/3x−1 . (1 point)
To graph the linear equation y = 2/3x - 1, we can start by plotting some points on the coordinate plane.
Let's choose some values of x and find the corresponding values of y.
When x = -3:
y = (2/3)(-3) - 1
y = -2 - 1
y = -3
So one point on the graph is (-3, -3).
When x = 0:
y = (2/3)(0) - 1
y = -1
So another point on the graph is (0, -1).
When x = 3:
y = (2/3)(3) - 1
y = 2 - 1
y = 1
So another point on the graph is (3, 1).
Using these points, we can plot them on the coordinate plane and draw a straight line through them.
Here is the graph:
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| . (3, 1)
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| . (0, -1)
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| (-3, -3)
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Graph the linear equation y=−3x+2 .(1 point)
To graph the linear equation y = -3x + 2, we can start by plotting some points on the coordinate plane.
Let's choose some values of x and find the corresponding values of y.
When x = -2:
y = -3(-2) + 2
y = 6 + 2
y = 8
So one point on the graph is (-2, 8).
When x = 0:
y = -3(0) + 2
y = 2
So another point on the graph is (0, 2).
When x = 2:
y = -3(2) + 2
y = -6 + 2
y = -4
So another point on the graph is (2, -4).
Using these points, we can plot them on the coordinate plane and draw a straight line through them.
Here is the graph:
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. | . (2, -4)
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| . (0, 2)
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| . (-2, 8)
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To graph the linear equation y = (2/3)x - 1, we can use the slope-intercept form, where the equation is in the form y = mx + b.
The slope (m) is 2/3, which means that for every increase of 3 units in the x-direction, the y-value increases by 2 units. The y-intercept (b) is -1, which is the point where the graph intersects the y-axis.
To graph the equation, we can start by plotting the y-intercept, which is the point (0, -1). This is where the line crosses the y-axis.
Next, we can use the slope to find additional points on the line. Since the slope is 2/3, we can use the rise over run method. Starting from the y-intercept (0, -1), we can go up 2 units and then go to the right 3 units. This gives us the point (3, 1).
We can repeat this process to find more points on the line. For example, from (3, 1), we can go up 2 units and right 3 units to get to the point (6, 3).
Now, we can connect these points to form a line.
To graph the linear equation y = (2/3)x - 1, follow these steps:
Step 1: Determine the slope and y-intercept.
The equation is already in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope (m) is 2/3, and the y-intercept (b) is -1.
Step 2: Plot the y-intercept.
The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is (0, -1). So, plot the point (0, -1) on the graph.
Step 3: Use the slope to find the next point.
Since the slope is 2/3, it means that for every change of 3 in the x-coordinate, there is a corresponding change of 2 in the y-coordinate. Start from the y-intercept (0, -1) and move 3 units to the right (positive x-direction) and then 2 units up (positive y-direction). This gives you a new point (3, 1).
Step 4: Draw the line through the two points.
Now that you have two points, (0,-1) and (3,1), you can draw a straight line through these points. Extend the line in both directions beyond the two points.
The resulting graph should be a straight line passing through the points (0,-1) and (3,1).