transform the linear equation -2y = 14 - 6x to slope-intercept form
To convert the linear equation -2y = 14 - 6x to slope-intercept form, we need to isolate y on one side of the equation.
First, we'll start by dividing both sides of the equation by -2 to solve for y:
-2y / -2 = (14 - 6x) / -2
y = -7 + 3x
Hence, the given linear equation -2y = 14 - 6x is re-written in slope-intercept form as y = 3x - 7.
write 0.4x + 0.2y = 0.6 in slope-intercept form
To convert the linear equation 0.4x + 0.2y = 0.6 to slope-intercept form, we need to isolate y on one side of the equation.
First, we'll start by subtracting 0.4x from both sides of the equation:
0.2y = -0.4x + 0.6
Then, we'll divide all terms by 0.2 to solve for y:
y = (-0.4x + 0.6) / 0.2
Simplifying the right side of the equation:
y = -2x + 3
Therefore, the given linear equation 0.4x + 0.2y = 0.6 is re-written in slope-intercept form as y = -2x + 3.
write the linear equation 3y = 6x - 18
To write the linear equation 3y = 6x - 18 in slope-intercept form, we need to isolate y on one side of the equation.
First, we'll start by dividing both sides of the equation by 3 to solve for y:
3y/3 = (6x - 18)/3
y = 2x - 6
Therefore, the given linear equation 3y = 6x - 18 is re-written in slope-intercept form as 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
To find the slope and y-intercept of the equation 9 + (27/2)x = (-3/2)y, we need to rewrite the equation in the slope-intercept form, which is y = mx + b.
First, we'll isolate y on one side of the equation by multiplying both sides by -2/3:
(-2/3)(9 + (27/2)x) = y
This simplifies to:
(-2/3)(9) + (-2/3)((27/2)x) = y
-6 + (-9x) = y
y = -9x - 6
Comparing this equation to y = mx + b, we can see that the slope (m) is -9 and the y-intercept (b) is -6.
Therefore, the slope of the equation is -9 and the y-intercept is (-6, 0).
(0,10) and (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.
To determine whether Annie's graph is correct, we can substitute the given points (0,10) and (1,7) into the equation 3x + y = 10 and check if they satisfy the equation.
For the point (0,10):
3(0) + 10 = 10
0 + 10 = 10
10 = 10
The equation is satisfied for the point (0,10).
For the point (1,7):
3(1) + 7 = 10
3 + 7 = 10
10 = 10
The equation is also satisfied for the point (1,7).
Since both given points satisfy the equation 3x + y = 10, we can conclude that Annie's graph is correct.
Option 3: Yes, Annie's graph is correct.
To transform the linear equation -2y = 14 - 6x to slope-intercept form, you need to rewrite the equation in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's go through the steps to convert the equation:
Step 1: Start with the given equation: -2y = 14 - 6x.
Step 2: To isolate y on one side of the equation, divide every term by -2. Remember, when you divide or multiply an equation by a negative number, you need to reverse the inequality sign. Dividing by -2 gives us:
(-2y) / -2 = (14 - 6x) / -2.
Simplifying this equation gives us: y = -7 + 3x.
So, the equation -2y = 14 - 6x transforms to y = -7 + 3x in slope-intercept form.
Thus, the equation y = -7 + 3x is now in slope-intercept form, where the slope is 3 and the y-intercept is -7.