Transform the linear equation −2y=14−6x
to slope-intercept form.(1 point)
To determine if Annie created the graph of 3x + y = 10 correctly, we need to compare her graph to the given information.
The equation 3x + y = 10 needs to be in slope-intercept form (y = mx + b) to identify the slope and y-intercept.
First, let's isolate y by subtracting 3x from both sides of the equation:
y = -3x + 10
From the given information, we see that the line passes through the points (0,10) and (1,7). The slope is the difference in y divided by the difference in x between these two points:
slope = (7 - 10) / (1 - 0) = -3 / 1 = -3
The y-intercept at (0,10) matches the y-intercept b = 10 in the equation 3x + y = 10.
Since Annie's graph has the correct slope and y-intercept as given by the equation 3x + y = 10 and the provided points, the correct answer is:
Option 3: Yes; Annie's graph is correct.
I apologize for the mistake. Let's correct it.
To transform the equation −2y = 14 − 6x into slope-intercept form, we need to isolate y.
First, let's rewrite the equation with the y term isolated:
−2y = −6x + 14
Next, divide through by -2 to solve for y:
-2y / -2 = (-6x + 14) / -2
y = 3x - 7
Therefore, the equation is in slope-intercept form y = 3x - 7.
To write the linear equation 3y = 6x - 18 in slope-intercept form (y = mx + b), we need to isolate y.
First, divide through by 3 to solve for y:
(3y) / 3 = (6x - 18) / 3
y = 2x - 6
Therefore, the equation is in slope-intercept form: y = 2x - 6.
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Write 0.4x+0.2y=0.6
in slope-intercept form.(1 point)
y=
To write the equation 0.4x + 0.2y = 0.6 in slope-intercept form (y = mx + b), we need to isolate y.
First, subtract 0.4x from both sides of the equation:
0.2y = -0.4x + 0.6
Next, divide through by 0.2 to solve for y:
(0.2y) / 0.2 = (-0.4x + 0.6) / 0.2
y = -2x + 3
Therefore, the equation is in slope-intercept form: y = -2x + 3.
Write the linear equation 3y=6x−18
in slope-intercept form.(1 point)
What is the slope and the y
-intercept of the equation 9+272x=−32y
. Write the y
-intercept as an ordered pair.(1 point)
The slope is
. The y
-intercept is (
).
Question
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. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 10 right parenthesis and left parenthesis 1 comma 7 right parenthesis.
Annie has created a graph of 3x+y=10
on the coordinate plane. Did Annie create her graph correctly?
Option 1: No; Annie's y
-intercept is correct but her slope is incorrect.
Option 2: No; Annie's slope is correct but her y
-intercept is incorrect.
Option 3: Yes; Annie's graph is correct.
Enter "1" for Option 1, "2" for Option 2, or "3" for Option 3.
To find the slope and the y-intercept of the equation 9 + 272x = -32y, we need to rewrite the equation in slope-intercept form (y = mx + b).
First, isolate y by dividing both sides by -32:
y = (-9 - 272x) / 32
Now, simplify the equation:
y = -9/32 - (272/32)x
y = -9/32 - 17x/8
From the equation, we can see that the coefficient of x is the slope, which is -17/8.
The y-intercept is the point at which the line intersects the y-axis. To find it, we substitute x = 0 into the equation:
y = -9/32
Therefore, the y-intercept is (0, -9/32).