Transform the linear equation 4x−8y=24 to slope-intercept form.
A. −8y=−4x+24
B. 4x−8y=24
C. y=1/2x−3
D. 4x−8y−24=0
To transform the linear equation 4x−8y=24 to slope-intercept form, we need to isolate y on one side of the equation.
First, add 8y to both sides of the equation:
4x−8y+8y=24+8y
4x=8y+24
Next, divide everything by 8 to isolate y:
4x/8=y+24/8
y=1/2x+3
Therefore, the slope-intercept form of the equation is C. y=1/2x−3.
Write y−2=3/2(x+2) in slope-intercept form.
A. y=3/2+5x
B. y=3/2x+5
C. y=3/2x+3/2
D. y=3/2x+6
To write the given equation y−2=3/2(x+2) in slope-intercept form y=mx+b, we need to simplify and isolate y on one side of the equation.
First, distribute 3/2 on the right side:
y − 2 = 3/2(x) + 3/2(2)
y − 2 = 3/2x + 3
Next, add 2 to both sides to isolate y:
y − 2 + 2 = 3/2x + 3 + 2
y = 3/2x + 5
Therefore, the slope-intercept form of the equation is B. y = 3/2x + 5.
Graph the equation 9−x=3/2y using slope-intercept form.
A. 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 3 right parenthesis, and left parenthesis 4 comma 2 right parenthesis.
B. 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 negative 3 right parenthesis, and left parenthesis 7 comma negative 1 right parenthesis.
C. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.
D. An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 6 right parenthesis and left parenthesis 3 comma 4 right parenthesis.
Let's first write the equation 9−x=3/2y in slope-intercept form.
We need to isolate y to do so.
9−x=3/2y
3/2y = 9−x
y = (9−x) * 2/3
y = 6 - 2/3x
Now that we have the equation in slope-intercept form y = -2/3x + 6, we can identify the correct graph choice.
Looking at the options:
A. Plotted points are (0,3) and (4,2). This does not match the equation.
B. Plotted points are (0,-3) and (7,-1). This does not match the equation.
C. Plotted points are (0,0) and (2,1). This does not match the equation.
D. Plotted points are (0,6) and (3,4). This matches the equation y = -2/3x + 6.
Therefore, the correct graph is D.
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 10 right parenthesis and left parenthesis 1 comma negative 7 right parenthesis.
Is this the correct graph of 3x−y=10 ?
A. No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10).
B. Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10).
C. No, it is not the correct graph because the slope is −3 and the y-intercept is (0, −10).
D. Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).
To determine if the given graph represents the equation 3x−y=10, we need to compare the equation to the attributes of the graph, specifically the slope and the y-intercept.
First, let's rewrite the equation 3x−y=10 in slope-intercept form (y = mx + b) by isolating y:
3x - y = 10
-y = -3x + 10
y = 3x - 10
From the equation, we can see that the slope is 3 and the y-intercept is (0, -10).
Comparing with the graph information:
- The graphed points given are (0, -10) and (1, -7).
- The slope of the graphed line connecting these points is upward, which seems to be a positive slope.
- The y-intercept of the graph matches the y-intercept from the equation.
Given the points provided, the positive slope, and the matching y-intercept, the correct answer is B. Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).
Identify the slope and the y-intercept of the equation 4x−3y=12.
A. The slope is −43, and the y-intercept is (0, 4).
B. The slope is 4, and the y-intercept is (0, 12).
C. The slope is 43, and the y-intercept is (0, −4).
D. The slope is 43, and the y-intercept is (0, 4).
To identify the slope and the y-intercept of the equation 4x−3y=12, first, we must rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
4x − 3y = 12
-3y = -4x + 12
y = 4/3x - 4
From the equation, we can see that the slope is 4/3 and the y-intercept is (0, -4).
Therefore, the correct answer is not listed among the options provided. The correct identification of the slope and y-intercept for the equation 4x−3y=12 is:
- The slope is 4/3, and the y-intercept is (0, -4).