Algebra 1 Practice Quiz

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.

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.

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.

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.

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

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).

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.

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.

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.

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.

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.

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.

Explanation
The equation 2y - 3x = 4 represents the line through the point (2,5) with a slope of 3. This can be determined by rearranging the equation to the form y = mx + b, where m is the slope. In this case, the slope is -3/2, which matches the given slope. Therefore, 2y - 3x = 4 is the correct equation for the line.

Explanation
The equation of a line can be found using the formula (y - y1) = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope of the line.

Using the points (3,4) and (1,-7), we can find the slope:
m = (y2 - y1) / (x2 - x1) = (-7 - 4) / (1 - 3) = -11 / -2 = 11/2

Now we can substitute the slope and one of the points into the formula to find the equation:
(y - 4) = (11/2)(x - 3)
2y - 8 = 11x - 33
11x - 2y = 25

Therefore, the correct answer is 11x - 2y = 25.

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.