Question
Graph the equation 9−x=3/2y using slope-intercept form
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Question Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point) Responses 4x−8y=24 4 x minus 8 y equals 24 y=12x−3 y equals Start Fraction 1 over 2 End Fraction x minus 3 4x−8y−24=0 4 x minus 8 y minus 24 equals 0 −8y=−4x+24
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Graph the equation 9 − x=3/2y using slope-intercept form
Answer
Identify the slope and the y-intercept of the equation 4x−3y=12.(1 point) Responses The slope is 4, and the y-intercept is (0, 12). The slope is 4, and the y-intercept is left parenthesis 0 comma 12 right parenthesis . The slope is 43, and the y-intercept is (0, 4). The slope is Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma 4 right parenthesis . The slope is 43, and the y-intercept is (0, −4). The slope is Start Fraction 4 over 3 End Fraction , and the y-intercept is left parenthesis 0 comma negative 4 right parenthesis . The slope is −43, and the y-intercept is (0, 4).
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GPT 3.5
To graph the equation 9 - x = (3/2)y, we need to rearrange it into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we subtract 9 from both sides to isolate x:
-x = (3/2)y - 9
Next, we multiply both sides by -1 to get x by itself:
x = -(3/2)y + 9
Now we can compare this equation with y = mx + b and identify the slope and y-intercept. The coefficient of y, (-3/2), is the slope, and the constant term, 9, is the y-intercept.
The slope is -3/2, which means that for every 2 units increase in x, y decreases by 3 units. The y-intercept is 9, which means that the line crosses the y-axis at the point (0, 9).
Now we can plot the y-intercept (0, 9) and use the slope to find additional points to draw the line.
Starting from the y-intercept (0, 9), we move 2 units to the right and 3 units down to find another point (2, 6).
Plot these two points (0, 9) and (2, 6) on a graph and draw a straight line passing through both points.
First, we subtract 9 from both sides to isolate x:
-x = (3/2)y - 9
Next, we multiply both sides by -1 to get x by itself:
x = -(3/2)y + 9
Now we can compare this equation with y = mx + b and identify the slope and y-intercept. The coefficient of y, (-3/2), is the slope, and the constant term, 9, is the y-intercept.
The slope is -3/2, which means that for every 2 units increase in x, y decreases by 3 units. The y-intercept is 9, which means that the line crosses the y-axis at the point (0, 9).
Now we can plot the y-intercept (0, 9) and use the slope to find additional points to draw the line.
Starting from the y-intercept (0, 9), we move 2 units to the right and 3 units down to find another point (2, 6).
Plot these two points (0, 9) and (2, 6) on a graph and draw a straight line passing through both points.
Answered by
GPT 3.5
To transform the equation 4x - 8y = 24 to slope-intercept form, we need to isolate y on one side of the equation.
First, let's subtract 4x from both sides:
-8y = -4x + 24
Next, divide every term by -8 to solve for y:
y = (-4x + 24) / -8
Simplifying further:
y = -4x/8 + 24/8
y = (-1/2)x + 3
Thus, the equation 4x - 8y = 24 is transformed to slope-intercept form as y = (-1/2)x + 3.
First, let's subtract 4x from both sides:
-8y = -4x + 24
Next, divide every term by -8 to solve for y:
y = (-4x + 24) / -8
Simplifying further:
y = -4x/8 + 24/8
y = (-1/2)x + 3
Thus, the equation 4x - 8y = 24 is transformed to slope-intercept form as y = (-1/2)x + 3.
Answered by
GPT 3.5
To graph the equation 9 − x = (3/2)y in slope-intercept form, we need to rearrange it to the form "y = mx + b", where "m" represents the slope and "b" represents the y-intercept.
First, let's isolate "y" on one side of the equation:
-x = (3/2)y - 9
Next, divide both sides by (3/2) to solve for "y":
-y = (2/3)x - 6
Now, let's multiply both sides by -1 to make the coefficient of "y" positive:
y = -(2/3)x + 6
In this form, we can identify that the slope is -(2/3) and the y-intercept is 6.
To graph this equation, we can start by plotting the y-intercept at the point (0, 6). Then, using the slope, we can find more points on the line. The slope -(2/3) means that for every 3 units increase in x, y decreases by 2 units.
Starting from the y-intercept (0, 6), we can move 3 units to the right and 2 units down to get the point (3, 4).
Plot these two points (0, 6) and (3, 4) on a graph and draw a straight line passing through both points.
First, let's isolate "y" on one side of the equation:
-x = (3/2)y - 9
Next, divide both sides by (3/2) to solve for "y":
-y = (2/3)x - 6
Now, let's multiply both sides by -1 to make the coefficient of "y" positive:
y = -(2/3)x + 6
In this form, we can identify that the slope is -(2/3) and the y-intercept is 6.
To graph this equation, we can start by plotting the y-intercept at the point (0, 6). Then, using the slope, we can find more points on the line. The slope -(2/3) means that for every 3 units increase in x, y decreases by 2 units.
Starting from the y-intercept (0, 6), we can move 3 units to the right and 2 units down to get the point (3, 4).
Plot these two points (0, 6) and (3, 4) on a graph and draw a straight line passing through both points.
Answered by
GPT 3.5
The correct response is: The slope is 4, and the y-intercept is (0, 4).
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