Algebra 1 Practice Quiz

1. (8,2) is a solution of x - 3y = 6

True

False

The point (8,2) is not a solution of the equation x - 3y = 6 because when we substitute x = 8 and y = 2 into the equation, we get 8 - 3(2) = 8 - 6 = 2, which is not equal to 6. Therefore, the statement is false.

Explanation

The point (8,2) is not a solution of the equation x - 3y = 6 because when we substitute x = 8 and y = 2 into the equation, we get 8 - 3(2) = 8 - 6 = 2, which is not equal to 6. Therefore, the statement is false.

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

On the y-axis

In the first Quadrant

In the fourth Quadrant

On the x-axis

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

Explanation

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

3. The graph of y = 2x + 3 passes through the origin.

True

False

The graph of y = 2x + 3 does not pass through the origin because when x = 0, y = 3. Therefore, the statement is false.

Explanation

The graph of y = 2x + 3 does not pass through the origin because when x = 0, y = 3. Therefore, the statement is false.

4. The price of a house increased by 7%. If the new price is $107,000, what was the original cost of the house?

$100,000

$114,490

$99,510

$93,000

The original cost of the house was $100,000. This can be determined by dividing the new price of $107,000 by 1.07, which represents a 7% increase. The result is $100,000, which is the original cost of the house.

Explanation

The original cost of the house was $100,000. This can be determined by dividing the new price of $107,000 by 1.07, which represents a 7% increase. The result is $100,000, which is the original cost of the house.

5. What is the slope of the line x = 7?

7

0

1/7

Undefined

The slope of a line is defined as the change in the y-coordinates divided by the change in the x-coordinates. In the given equation x = 7, the value of x is always 7, meaning that there is no change in the x-coordinate. Therefore, the change in the y-coordinate is also undefined, resulting in an undefined slope.

Explanation

The slope of a line is defined as the change in the y-coordinates divided by the change in the x-coordinates. In the given equation x = 7, the value of x is always 7, meaning that there is no change in the x-coordinate. Therefore, the change in the y-coordinate is also undefined, resulting in an undefined slope.

6. (-3, 7) is located in quadrant:

I

II

III

IV

The point (-3, 7) is located in quadrant II because the x-coordinate (-3) is negative and the y-coordinate (7) is positive. In quadrant II, the x-coordinate is negative and the y-coordinate is positive.

Explanation

The point (-3, 7) is located in quadrant II because the x-coordinate (-3) is negative and the y-coordinate (7) is positive. In quadrant II, the x-coordinate is negative and the y-coordinate is positive.

7. Find the slope of the line 6x-2y=12-2y?

6

1/6

0

Undefined

The given equation is in the form 6x - 2y = 12 - 2y. By simplifying the equation, we can see that the variable "y" cancels out on both sides, resulting in 6x = 12. Since there is no "y" term in the equation, the slope of the line is undefined.

Explanation

The given equation is in the form 6x - 2y = 12 - 2y. By simplifying the equation, we can see that the variable "y" cancels out on both sides, resulting in 6x = 12. Since there is no "y" term in the equation, the slope of the line is undefined.

8. What quadrant does the line 5x + 3y = 15 not pass through?

I

II

III

IV

The line 5x + 3y = 15 does not pass through quadrant III. This is because in quadrant III, both x and y values are negative. Plugging in negative values for x and y into the equation would result in a sum greater than 15, making it impossible for the line to pass through quadrant III.

Explanation

The line 5x + 3y = 15 does not pass through quadrant III. This is because in quadrant III, both x and y values are negative. Plugging in negative values for x and y into the equation would result in a sum greater than 15, making it impossible for the line to pass through quadrant III.

9. What is the slope of the line through (6,5) and (9,1)?

4/3

-3/4

-4/3

3/4

The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (6,5) and (9,1). Plugging these values into the formula, we get (1 - 5) / (9 - 6) = -4 / 3. Therefore, the slope of the line is -4/3.

Explanation

The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (6,5) and (9,1). Plugging these values into the formula, we get (1 - 5) / (9 - 6) = -4 / 3. Therefore, the slope of the line is -4/3.

10. Find an equation of the line through (25) with a slope of .

Y - x = 4

2y - 3x = 4

3x - 2y = 4

X - y = 4

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where:

m is the slope of the line

(x1, y1) is a point on the line

In this case, we have m = 3/2 and (x1, y1) = (2, 5). Substituting these values into the point-slope form, we get:

y - 5 = (3/2)(x - 2)

Multiplying both sides by 2 to eliminate the fraction, we get:

2y - 10 = 3x - 6

Rearranging the terms, we get the equation in standard form:

2y - 3x = 4

Explanation

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where:

m is the slope of the line

(x1, y1) is a point on the line

In this case, we have m = 3/2 and (x1, y1) = (2, 5). Substituting these values into the point-slope form, we get:

y - 5 = (3/2)(x - 2)

Multiplying both sides by 2 to eliminate the fraction, we get:

2y - 10 = 3x - 6

Rearranging the terms, we get the equation in standard form:

2y - 3x = 4

11. Find an equation of a line through (0,2) parallel to the line 3x-6y=1.

2y - x = 4

2y x = 2x

Y - 2x = 2

Y - 2x = 4

The equation of a line parallel to 3x-6y=1 can be found by keeping the same slope. The slope of the given line is 3/6 or 1/2. Using the point-slope form of a linear equation, we can substitute the slope and the coordinates of the given point (0,2) to find the equation. Therefore, the equation of the line parallel to 3x-6y=1 and passing through (0,2) is 2y - x = 4.

Explanation

The equation of a line parallel to 3x-6y=1 can be found by keeping the same slope. The slope of the given line is 3/6 or 1/2. Using the point-slope form of a linear equation, we can substitute the slope and the coordinates of the given point (0,2) to find the equation. Therefore, the equation of the line parallel to 3x-6y=1 and passing through (0,2) is 2y - x = 4.

12. Find an equation for the line with slope and y-intercept 3.

4x - 3y = -3

4x - 3y = -9

3y - 4x = -3

3y - 4x = -9

The equation 4x - 3y = -9 represents the line with a slope of 4 and a y-intercept of 3. This can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, when we rearrange the equation, we get y = (4/3)x + 3, which matches the slope and y-intercept given in the question. Therefore, 4x - 3y = -9 is the correct equation for the line.

Explanation

The equation 4x - 3y = -9 represents the line with a slope of 4 and a y-intercept of 3. This can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, when we rearrange the equation, we get y = (4/3)x + 3, which matches the slope and y-intercept given in the question. Therefore, 4x - 3y = -9 is the correct equation for the line.

13. What is the x-intercept of x =2?

(0,2)

(2,0)

(0,0)

There is no x-intercept

The equation x = 2 represents a vertical line passing through the point (2,0) on the x-axis. Since this line is parallel to the y-axis, it does not intersect the x-axis at any point. Therefore, there is no x-intercept for the given equation.

Explanation

The equation x = 2 represents a vertical line passing through the point (2,0) on the x-axis. Since this line is parallel to the y-axis, it does not intersect the x-axis at any point. Therefore, there is no x-intercept for the given equation.

14. What is the y- intercept for 5y = 4x - 20?

(5,0)

(0,5)

(-4,0)

(0,-4)

To find the y-intercept, we first set the value of x to 0 in the equation. This eliminates the x-term, leaving us with an equation only involving y. We then solve for y to determine the y-coordinate where the graph intersects the y-axis, representing the y-intercept. In this case, when x is 0, y is calculated to be -4. Therefore, the y-intercept is the point (0, -4).

Explanation

To find the y-intercept, we first set the value of x to 0 in the equation. This eliminates the x-term, leaving us with an equation only involving y. We then solve for y to determine the y-coordinate where the graph intersects the y-axis, representing the y-intercept. In this case, when x is 0, y is calculated to be -4. Therefore, the y-intercept is the point (0, -4).

15. Find an equation of a line through (3,4) and (1,-7).

11x - 2y = -5

11x - 2y = -1

2x - 11y = -38

11x - 2y = 25

To find the equation of a line, we need to determine its slope and y-intercept.

Calculate the slope (m):

m = (y2 - y1) / (x2 - x1) m = (-7 - 4) / (1 - 3) m = -11 / -2 m = 11/2

Use the point-slope form:

y - y1 = m(x - x1) y - 4 = (11/2)(x - 3)

Simplify to slope-intercept form (y = mx + b):

y - 4 = (11/2)x - 33/2 y = (11/2)x - 33/2 + 4 y = (11/2)x - 25/2

Convert to standard form (Ax + By = C):

-11/2x + y = -25/2 11x - 2y = 25

Explanation

To find the equation of a line, we need to determine its slope and y-intercept.

Calculate the slope (m):

m = (y2 - y1) / (x2 - x1) m = (-7 - 4) / (1 - 3) m = -11 / -2 m = 11/2

Use the point-slope form:

y - y1 = m(x - x1) y - 4 = (11/2)(x - 3)

Simplify to slope-intercept form (y = mx + b):

y - 4 = (11/2)x - 33/2 y = (11/2)x - 33/2 + 4 y = (11/2)x - 25/2

Convert to standard form (Ax + By = C):

-11/2x + y = -25/2 11x - 2y = 25