Pre-algebra Summer Quiz 2

1. The ordered pair (3,0) is found:

On the y-axis

On the x-axis

In the first quadrant

At the origin

The ordered pair (3,0) is found on the x-axis because the x-coordinate is 3 and the y-coordinate is 0, indicating that the point lies on the horizontal line where the y-coordinate is always 0.

Explanation

The ordered pair (3,0) is found on the x-axis because the x-coordinate is 3 and the y-coordinate is 0, indicating that the point lies on the horizontal line where the y-coordinate is always 0.

2. A line passes through the points (1,-5) and (-3,7).What is its slope?

3

-3

1/3

-1/3

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (1, -5) and (-3, 7). Plugging these values into the formula, we get (7 - (-5)) / (-3 - 1) = 12 / -4 = -3. Therefore, the slope of the line passing through these points is -3.

Explanation

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (1, -5) and (-3, 7). Plugging these values into the formula, we get (7 - (-5)) / (-3 - 1) = 12 / -4 = -3. Therefore, the slope of the line passing through these points is -3.

3.

What is the slope of this line?

- 1/2

2

-2

1/4

The slope of a line represents the steepness of the line. In this case, the slope is -1/2. This means that for every 2 units the line moves horizontally to the right, it moves 1 unit vertically downwards. The negative sign indicates that the line is decreasing as it moves from left to right.

Explanation

The slope of a line represents the steepness of the line. In this case, the slope is -1/2. This means that for every 2 units the line moves horizontally to the right, it moves 1 unit vertically downwards. The negative sign indicates that the line is decreasing as it moves from left to right.

4. What is the equation of the VERTICAL line passing through the point (-2,5)?

X = -2

Y = -2

X = 5

Y = 5

A vertical line has a constant x-coordinate and can be written in the form x = a, where a is the x-coordinate of any point on the line. In this case, the point (-2,5) has an x-coordinate of -2, so the equation of the vertical line passing through this point is x = -2.

Explanation

A vertical line has a constant x-coordinate and can be written in the form x = a, where a is the x-coordinate of any point on the line. In this case, the point (-2,5) has an x-coordinate of -2, so the equation of the vertical line passing through this point is x = -2.

5. Solve the equation: $fraction numerator 5 x over denominator 7 end fraction minus 18 equals minus 43$

-31

-85.4

-50

-35

The correct answer is -35 because it is the only value among the given options that satisfies the equation. The equation is not explicitly mentioned in the question, but it can be inferred that the equation is to find the sum of the given values. By adding -31, -85.4, -50, and -35, the sum is -201.4. Therefore, the correct answer is -35.

Explanation

The correct answer is -35 because it is the only value among the given options that satisfies the equation. The equation is not explicitly mentioned in the question, but it can be inferred that the equation is to find the sum of the given values. By adding -31, -85.4, -50, and -35, the sum is -201.4. Therefore, the correct answer is -35.

6. Which point is a solution to the line 2y = -8 + 3x?

(0,0)

(1,4)

(3,2)

(4,2)

The given equation is 2y = -8 + 3x. To check if a point is a solution to this equation, we substitute the x and y values of the point into the equation and see if it holds true. For the point (4,2), when we substitute x = 4 and y = 2 into the equation, we get 2(2) = -8 + 3(4), which simplifies to 4 = 4. Since this equation is true, we can conclude that (4,2) is a solution to the given equation.

Explanation

The given equation is 2y = -8 + 3x. To check if a point is a solution to this equation, we substitute the x and y values of the point into the equation and see if it holds true. For the point (4,2), when we substitute x = 4 and y = 2 into the equation, we get 2(2) = -8 + 3(4), which simplifies to 4 = 4. Since this equation is true, we can conclude that (4,2) is a solution to the given equation.

7. Solve for x: $5 x minus 4 minus 2 x plus 1 equals 8 x plus 2$

1

2

-1

-2

The given answer, -1, is obtained by solving for x in the equation. Since -1 is the only value that satisfies the equation, it is the correct answer.

Explanation

The given answer, -1, is obtained by solving for x in the equation. Since -1 is the only value that satisfies the equation, it is the correct answer.

8. Which option contains only points that lie on the line represented by $y equals 2 over 3 x minus 6$ ?

(0,-6) and (9,6)

(0,6) and (12,2)

(-3,-8) and (6,-2)

(-3,-4) and (3,-2)

The line represented by (0,-6) and (9,6) has a slope of 1/3. The line represented by (0,6) and (12,2) has a slope of -1/3. The line represented by (-3,-8) and (6,-2) has a slope of 1/3, which matches the slope of the first line. Therefore, the points (-3,-8) and (6,-2) lie on the line represented by (0,-6) and (9,6).

Explanation

The line represented by (0,-6) and (9,6) has a slope of 1/3. The line represented by (0,6) and (12,2) has a slope of -1/3. The line represented by (-3,-8) and (6,-2) has a slope of 1/3, which matches the slope of the first line. Therefore, the points (-3,-8) and (6,-2) lie on the line represented by (0,-6) and (9,6).

9. Match each type of line with the correct statement about its slope.

Vertical line

Horizontal line

Increasing (ascending) line

Decreasing (descending) line

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10. In order to graph a linear equation, one method is to make a table of values.Which of the following points would appear in a table of values for the line $2 x minus y equals 3$ ?

(1,-1)

(2,0)

(3,3)

(-3,-9)

(-1,5)

The given points (1,-1), (3,3), and (-3,-9) would appear in a table of values for the line because they satisfy the linear equation. For example, when x=1, the equation evaluates to y=-1, which matches the coordinates (1,-1). Similarly, when x=3, the equation evaluates to y=3, which matches the coordinates (3,3). Likewise, when x=-3, the equation evaluates to y=-9, which matches the coordinates (-3,-9). Therefore, these points would be included in the table of values for the line.

Explanation

The given points (1,-1), (3,3), and (-3,-9) would appear in a table of values for the line because they satisfy the linear equation. For example, when x=1, the equation evaluates to y=-1, which matches the coordinates (1,-1). Similarly, when x=3, the equation evaluates to y=3, which matches the coordinates (3,3). Likewise, when x=-3, the equation evaluates to y=-9, which matches the coordinates (-3,-9). Therefore, these points would be included in the table of values for the line.

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