Transform the linear equation - 2y = 14 - 6x to slope-intercept form.
To transform the linear equation -2y = 14 - 6x to slope-intercept form, we need to solve for y.
First, divide both sides of the equation by -2 to isolate y:
-2y = 14 - 6x
Dividing both sides by -2:
y = (14 - 6x)/-2
Simplifying:
y = -7 + 3x
The equation is now in slope-intercept form, y = mx + b, where m is the slope (3 in this case) and b is the y-intercept (-7 in this case).
Transform the linear equation - 2y = 14 - 6x to slope-intercept form.
y =__
To transform the linear equation -2y = 14 - 6x to slope-intercept form, we need to solve for y.
First, divide both sides of the equation by -2 to isolate y:
-2y = 14 - 6x
Dividing both sides by -2:
y = (14 - 6x)/-2
Simplifying:
y = -7 + 3x
Therefore, the equation in slope-intercept form is:
y = 3x - 7
Write 0.4x + 0.2y = 0.6 in slope-intercept form.
y =__
To write the equation 0.4x + 0.2y = 0.6 in slope-intercept form, we need to solve for y.
First, subtract 0.4x from both sides:
0.2y = -0.4x + 0.6
Next, divide both sides by 0.2:
y = (-0.4/0.2)x + (0.6/0.2)
Simplifying:
y = -2x + 3
Therefore, the equation in slope-intercept form is:
y = -2x + 3
Write the linear equation 3y = 6x - 18 in slope-intercept form.
__
To write the linear equation 3y = 6x - 18 in slope-intercept form, we need to solve for y.
First, divide both sides of the equation by 3 to isolate y:
3y = 6x - 18
Dividing both sides by 3:
y = (6x - 18)/3
Simplifying:
y = 2x - 6
Therefore, the equation in slope-intercept form is:
y = 2x - 6
What is the slope and the y-intercept of the equation 9 + 27/2x = -3/2y. Write the y-intercept as an ordered pair.
The slope is __. The y-intercept is (__).
To find the slope and the y-intercept of the equation 9 + 27/2x = -3/2y, we need to rearrange it in the slope-intercept form, which is y = mx + b.
First, let's isolate y:
9 + (27/2)x = (-3/2)y
Divide both sides by (-3/2):
(-2/3)(9 + (27/2)x) = y
Multiplying (-2/3) by each term inside the parentheses:
y = -6 - (27/3)x
Simplifying further:
y = -6 - 9x
Comparing it to the slope-intercept form, we can see that the slope (m) is -9 and the y-intercept (b) is -6.
Therefore, the slope is -9 and the y-intercept is (-6, 0).
The y-intercept is wrong
Apologies for the mistake.
To find the y-intercept, we need to set x = 0 in the equation and solve for y.
9 + (27/2)(0) = (-3/2)y
9 = (-3/2)y
Dividing both sides by (-3/2):
y = (-2/3)(9)
y = -6
Therefore, the y-intercept is (-6, 0).
To find the slope, we need to rearrange the equation in slope-intercept form: y = mx + b
From the given equation 9 + (27/2)x = (-3/2)y, we can isolate y:
(-3/2)y = 9 + (27/2)x
Dividing both sides by (-3/2):
y = -(2/3)(9 + (27/2)x)
Simplifying:
y = -(2/3)(9) - (2/3)(27/2)x
y = -6 - 9x
Therefore, the slope is -9 and the y-intercept is (-6, 0).
(0,10)
(1,7)
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.
Option __
To determine if Annie created the graph correctly, we can substitute the given points (0,10) and (1,7) into the linear equation 3x + y = 10 and see if they satisfy the equation.
For the point (0,10):
3(0) + 10 = 10
0 + 10 = 10
10 = 10
For the point (1,7):
3(1) + 7 = 10
3 + 7 = 10
10 = 10
Both points satisfy the equation, so Annie's graph is correct.
Therefore, the correct option is:
Option 3: Yes; Annie's graph is correct.
Transform the linear equation 4x - 8y = 24 to slope-intercept form.
To transform the linear equation 4x - 8y = 24 to slope-intercept form, we need to solve for y.
First, isolate -8y by subtracting 4x from both sides of the equation:
-8y = -4x + 24
Next, divide both sides by -8 to solve for y:
y = (-4x + 24)/-8
Simplifying:
y = -4x/-8 + 24/-8
y = 1/2x - 3
Therefore, the equation in slope-intercept form is:
y = 1/2x - 3.