Which procedure could be used to graph the following equation?
y equals one-fourth x minus 1
A. Plot the y-intercept (0, –1) and use the slope of one-fourth to find a second point.
B. Plot the y-intercept left parenthesis 0 comma one-fourth right parenthesis and use the slope of –1 to find a second point.
C. Plot the x-interceptleft parenthesis one-fourth comma 0 right parenthesis and use the slope of –1 to find a second point.
D. Plot the x-intercept (–1, 0) and use the slope of one-fourth to find a second point.
The correct answer is A. Plot the y-intercept (0, -1) and use the slope of one-fourth to find a second point.
Which equation defines the graph of y = x3 after it is shifted vertically 5 units down and horizontally 4 units left?
A. y = (x – 4)3 – 5
B. y = (x + 5)3 – 4
C. y = (x + 5)3 + 4
D. y = (x + 4)3 – 5
The correct answer is A. y = (x - 4)3 - 5.
The correct answer is A. Plot the y-intercept (0, –1) and use the slope of one-fourth to find a second point.
To graph the equation y = (1/4)x - 1, start by plotting the y-intercept, which is the point where the line intersects the y-axis. In this case, the y-intercept is (0, -1), where x = 0 and y = -1.
Next, use the slope of 1/4 to find a second point. The slope represents the ratio of change in y to the change in x. In this case, for every 1 unit increase in x, y will increase by 1/4.
To find the second point, start from the y-intercept (0, -1) and move 1 unit to the right. Since the slope is 1/4, you will move 1/4 units upwards. This gives you the point (1, -3/4).
You can plot these two points on a graph and draw a straight line through them to complete the graph of the equation y = (1/4)x - 1.
To graph the equation y = 1/4x - 1, we can follow these steps:
1. Identify the y-intercept: The y-intercept is the point where the graph crosses the y-axis, which can be found by setting x = 0 in the equation. In this case, when x = 0, y = 1/4(0) - 1 = -1. So, the y-intercept is (0, -1).
2. Determine the slope: The slope of the equation is the coefficient of x, which is 1/4. The slope is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
3. Use the slope to find a second point: Since we already have the y-intercept as one point on the line, we can use the slope to find another point. To do this, we can move vertically up or down by the numerator of the slope (rise), and then move horizontally left or right by the denominator of the slope (run).
Given the options, we can eliminate B and C because they don't have the correct y-intercept.
Let's check the remaining options:
A. Plot the y-intercept (0, -1) and use the slope of 1/4 to find a second point.
If we use the slope of 1/4 to find a second point, we can move up 1 unit (rise) and then move right 4 units (run) from the y-intercept.
So, the second point would be (4, 0).
D. Plot the x-intercept (-1, 0) and use the slope of 1/4 to find a second point.
To find a second point using the slope of 1/4, we can move down 1 unit (rise) and then move right 4 units (run) from the x-intercept.
So, the second point would be (3, -1).
Based on the calculation, option A is the correct answer.
The procedure to graph the equation y = 1/4x - 1 is to plot the y-intercept (0, -1) and use the slope of 1/4 to find a second point.