The graph of the equation y = -20 is a ____________ line.
The graph of the equation y = -20 is a horizontal line.
Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.
Question 1 options:
A) x-intercept = -2; y-intercept = 8
B) x-intercept = -8; y-intercept = 8
C) x-intercept = 2; y-intercept = -8
D) x-intercept = 2; y-intercept = 8
The equation y = -20 represents a horizontal line that passes through the y-axis at y = -20. Since this line is parallel to the x-axis, it does not intersect the x-axis, so there is no x-intercept. Therefore, the correct answer is:
C) There is no x-intercept. The y-intercept is y = -20.
Solve the equation using both the addition and multiplication properties of equality.
5x - 8 = 56 - 3x
To solve the equation 5x - 8 = 56 - 3x using the addition and multiplication properties of equality, we will first use the addition property to isolate the variable terms on one side of the equation.
First, we can add 3x to both sides of the equation to eliminate the variable term on the right side:
5x - 8 + 3x = 56 - 3x + 3x
Simplifying this equation, we get:
8x - 8 = 56
Next, we use the addition property to add 8 to both sides of the equation to eliminate the constant term on the left side:
8x - 8 + 8 = 56 + 8
Simplifying this equation, we get:
8x = 64
Now, we can use the multiplication property of equality to solve for x. We will multiply both sides of the equation by the reciprocal of the coefficient of x, which is 1/8:
(1/8)(8x) = (1/8)(64)
Simplifying this equation, we get:
x = 8
Therefore, the solution to the equation 5x - 8 = 56 - 3x is x = 8.
Find the x-intercept and the y-intercept of the graph of the equation. Do not graph the equation.
-2x + 2y = 10
To find the x-intercept, we set y = 0 and solve for x.
-2x + 2(0) = 10
-2x = 10
x = 10 / -2
x = -5
So the x-intercept is -5.
To find the y-intercept, we set x = 0 and solve for y.
-2(0) + 2y = 10
0 + 2y = 10
2y = 10
y = 10 / 2
y = 5
So the y-intercept is 5.
Therefore, the x-intercept is -5 and the y-intercept is 5.
Solve the equation for y.
4x + y = 20
To solve the equation 4x + y = 20 for y, we need to isolate y on one side of the equation.
First, we can subtract 4x from both sides of the equation:
4x + y - 4x = 20 - 4x
Simplifying this equation, we get:
y = 20 - 4x
Therefore, the equation can be solved for y as y = 20 - 4x.
The graph of the equation x = -42 is a ____________ line.
The graph of the equation x = -42 is a vertical line.
Determine whether the ordered pair is a solution of the given equation.
(-3, 6)
3x + 4y = 15
To determine if the ordered pair (-3, 6) is a solution of the equation 3x + 4y = 15, we substitute the values of x and y into the equation and check if it is true.
Substituting x = -3 and y = 6 into the equation, we get:
3(-3) + 4(6) = 15
-9 + 24 = 15
15 = 15
Since the equation is true when the ordered pair (-3, 6) is substituted, we can conclude that (-3, 6) is indeed a solution of the equation.
Find the y- and x-intercepts for the equation. Then graph the equation.
-4x - 12y = 12
Question 8 options:
A)
(0, 1); (-3, 0)
B)
(0, 1); (3, 0)
C)
(0, -1); (-3, 0)
D)
(0, -1); (3, 0)
To find the x-intercept, we set y equal to zero and solve for x.
-4x - 12(0) = 12
-4x = 12
x = 12/(-4)
x = -3
So the x-intercept is (-3, 0).
To find the y-intercept, we set x equal to zero and solve for y.
-4(0) - 12y = 12
-12y = 12
y = 12/(-12)
y = -1
So the y-intercept is (0, -1).
Therefore, the correct answer is:
D) (0, -1); (3, 0)
Now, let's graph the equation.
To graph the line -4x - 12y = 12, we can rewrite it in slope-intercept form (y = mx + b) by solving for y:
-4x - 12y = 12
-12y = 4x + 12
y = -(1/3)x - 1
The slope is -(1/3) and the y-intercept is -1. We can plot the y-intercept at (0, -1) and then use the slope to find another point on the line. Since the slope is -(1/3), we can go down 1 unit and to the right 3 units. This gives us the point (3, 0).
So, the graph of the equation -4x - 12y = 12 is a line passing through the points (0, -1) and (3, 0).
Here is the graph:
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Solve the equation using both the addition and multiplication properties of equality.
5n - 8 = 37
To solve the equation 5n - 8 = 37 using the addition and multiplication properties of equality, we will first use the addition property to isolate the variable term on one side of the equation.
First, we can add 8 to both sides of the equation to eliminate the constant term on the left side:
5n - 8 + 8 = 37 + 8
Simplifying this equation, we get:
5n = 45
Next, we can use the multiplication property of equality to solve for n. We will multiply both sides of the equation by the reciprocal of the coefficient of n, which is 1/5:
(1/5)(5n) = (1/5)(45)
Simplifying this equation, we get:
n = 9
Therefore, the solution to the equation 5n - 8 = 37 is n = 9.
Give the ordered pairs that correspond to the points labeled in the figure.
Question 10 options:
A)
A = (2, 7), B = (3, -4)
B)
A = (2, 7), B = (-4, 3)
C)
A = (7, 20), B = (3, -4)
D)
A = (2, 3), B = (7, 3)