1.) Which is the equation of the line that contains the points (0,3) and (-2,4)?
A.
x+2y=6
B.
2x+y=3
C.
2x+y=0
D.
x-2y=6
2.) Which statement is true of the equation that follows?
y-6 = -3(x + 1)
A.
The slope is 3, and the y-intercept is -6.
B.
The slope is 3, and the y-intercept is 1.
C.
The slope is -3, and the y-intercept is 3.
D.
The slope is -3, and the y-intercept is 1.
3.) Which is an equation of the line that contains the points (0, 2) and (4, 0)?
A.
y = 2x + 4
B.
y = 2x + 2
C.
y= -1/2 x + 4
D.
y = -1/2 x +2
4.) A juice machine dispenses the same amount of juice into a cup each time the machine is used. The equation that follows describes the relationship between the number of cups (x) into which juice is dispensed and the gallons of juice (y) remaining in the machine:
x+12y=180
How many gallons of juice are in the machine when it is full?
A.
12
B.
15
C.
168
D.
180
Thanks so much! (:
1. A
2. C
3. D
4.B
Whts the answer
Sure! Let's go through each question step-by-step:
1.) To find the equation of the line that contains the points (0,3) and (-2,4), we can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
Substituting the values of the points, we get: m = (4 - 3) / (-2 - 0) = 1 / (-2) = -1/2.
Now that we have the slope, we can plug it into the equation y = mx + b and substitute the coordinates of one of the points to solve for b.
Using the point (0,3), we have: 3 = (-1/2)(0) + b.
This simplifies to: 3 = b.
So the y-intercept (b) is equal to 3.
Therefore, the equation of the line that contains the points (0,3) and (-2,4) is: y = -1/2x + 3.
Looking at the answer choices, the correct option is D. x - 2y = 6.
2.) Given the equation y - 6 = -3(x + 1), we can determine the slope and y-intercept by rearranging the equation into slope-intercept form (y = mx + b).
Start by simplifying the equation:
y - 6 = -3x - 3
y = -3x - 3 + 6
y = -3x + 3
Comparing this equation to y = mx + b, we can see that the slope (m) is -3 and the y-intercept (b) is 3. Hence, the correct option is C. The slope is -3, and the y-intercept is 3.
3.) Let's find the equation of the line that passes through the points (0, 2) and (4, 0). Again, we'll use the slope-intercept form (y = mx + b).
First, determine the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
Substituting the coordinates, we have: m = (0 - 2) / (4 - 0) = -2 / 4 = -1/2.
Now, substitute the slope (m) and one of the points into the equation y = mx + b. Let's use the point (0, 2) since it simplifies the equation.
Substituting for x, y, and m, we get: 2 = (-1/2)(0) + b.
This simplifies to: 2 = b.
So the y-intercept (b) is equal to 2.
Therefore, the equation of the line that contains the points (0,2) and (4,0) is: y = -1/2x + 2.
Looking at the answer choices, the correct option is D. y= -1/2 x + 2.
4.) The equation x + 12y = 180 represents the relationship between the number of cups (x) into which juice is dispensed and the gallons of juice (y) remaining in the machine.
To find out the amount of juice in the machine when it is full, we need to find the value of y when x equals the maximum number of cups.
By rearranging the equation, we can solve for y:
12y = 180 - x
y = (180 - x)/12
Since we are looking for the number of gallons of juice when the machine is full, we need to find the value of y when x is at its maximum. However, without any additional information given in the question, we cannot determine the maximum value of x or the total number of cups the machine can dispense. Therefore, we cannot determine the exact number of gallons of juice in the machine when it is full. Thus, none of the answer choices (A, B, C, or D) are correct.
I hope this helps! Let me know if you have any other questions.