The given equation is in slope-intercept form: y = mx + b.
Comparing with the given equation, we can see that m = -2 and b = -1.
Therefore, the slope of the equation is -2, and the y-intercept is (0, -1).
y=−2x−1
5 answers
6x+2y=60
To rewrite the equation in slope-intercept form y = mx + b, let's rearrange the given equation.
6x + 2y = 60
First, subtract 6x from both sides to isolate the term with the variable y.
2y = -6x + 60
Next, divide both sides by 2 to solve for y.
y = (-6x + 60)/2
Simplifying further,
y = -3x + 30
Comparing this equation to the slope-intercept form y = mx + b, we can determine that the slope (m) for the given equation is -3, and the y-intercept (b) is (0, 30).
6x + 2y = 60
First, subtract 6x from both sides to isolate the term with the variable y.
2y = -6x + 60
Next, divide both sides by 2 to solve for y.
y = (-6x + 60)/2
Simplifying further,
y = -3x + 30
Comparing this equation to the slope-intercept form y = mx + b, we can determine that the slope (m) for the given equation is -3, and the y-intercept (b) is (0, 30).
Solve the system of equations.
3x+4y=48
6x+2y=60
3x+4y=48
6x+2y=60
To solve the system of equations:
3x + 4y = 48 --------(1)
6x + 2y = 60 --------(2)
Let's multiply equation (1) by 2, and equation (2) by 4 to eliminate the variable y:
2*(3x + 4y) = 2*48
4*(6x + 2y) = 4*60
This simplifies to:
6x + 8y = 96 --------(3)
24x + 8y = 240 --------(4)
Now, subtract equation (3) from equation (4):
(24x + 8y) - (6x + 8y) = 240 - 96
This simplifies to:
24x - 6x = 144
Combining like terms:
18x = 144
Divide both sides by 18:
x = 8
Now, substitute the value of x into either equation (1) or (2) to solve for y. Let's use equation (2):
6x + 2y = 60
6(8) + 2y = 60
48 + 2y = 60
Subtract 48 from both sides:
2y = 12
Divide both sides by 2:
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
3x + 4y = 48 --------(1)
6x + 2y = 60 --------(2)
Let's multiply equation (1) by 2, and equation (2) by 4 to eliminate the variable y:
2*(3x + 4y) = 2*48
4*(6x + 2y) = 4*60
This simplifies to:
6x + 8y = 96 --------(3)
24x + 8y = 240 --------(4)
Now, subtract equation (3) from equation (4):
(24x + 8y) - (6x + 8y) = 240 - 96
This simplifies to:
24x - 6x = 144
Combining like terms:
18x = 144
Divide both sides by 18:
x = 8
Now, substitute the value of x into either equation (1) or (2) to solve for y. Let's use equation (2):
6x + 2y = 60
6(8) + 2y = 60
48 + 2y = 60
Subtract 48 from both sides:
2y = 12
Divide both sides by 2:
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.