Which equation represents the graph? (1 point) Responses y=3x+5 y is equal to 3 x plus 5 y=12x−1 y is equal to 1 half x minus 1 y=−45x+3 y is equal to negative 4 fifths x plus 3 y=54x+3 y is equal to 5 fourths x plus 3 Skip to navigation page 2 of 2
The equation that represents the graph is y=12x−1.
Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.
a. What is the rate of change (slope) for the scenario?
b. What is the y-intercept for this scenario?
c. Write an equation for the scenario in slope-intercept form.
d. Write an equation in standard form.
a. To find the rate of change (slope), we can use the formula:
Slope = (change in y)/(change in x)
From the given information, the change in the water level is 45 ft - 10 ft = 35 ft, and the change in the number of days is 3 days - 10 days = -7 days (since the water level decreased during this period).
So, the slope is:
Slope = (35 ft) / (-7 days) = -5 ft/day
b. The y-intercept represents the initial water level before the drought began, which is given to be 60 feet.
So, the y-intercept is 60.
c. Using the slope-intercept form of the equation (y = mx + b), we have:
y = -5x + 60
d. To write the equation in standard form (Ax + By = C), we can multiply both sides of the equation from part c) by -1:
-5x + y = -60
Therefore, the equation in standard form is:
5x - y = 60
d. is wrong
Apologies for the mistake. Let's correct part d:
To write the equation in standard form (Ax + By = C), we need to rearrange the equation from part c) and express it in the form Ax + By = C.
The slope-intercept form is:
y = -5x + 60
To convert it to standard form, we can rearrange the equation and move all the terms to one side:
5x + y = 60
Multiplying both sides of the equation by -1, we get:
-5x - y = -60
Hence, the equation in standard form is:
-5x - y = -60
Without a graph provided, it is not possible to determine which equation represents the graph.
To determine which equation represents the graph, you can compare the slope-intercept form of each equation with the information given from the graph.
The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Looking at the options:
1. y = 3x + 5
This equation has a slope of 3 and a y-intercept of 5.
2. y = 12x - 1
This equation has a slope of 12 and a y-intercept of -1.
3. y = -45x + 3
This equation has a slope of -45 and a y-intercept of 3.
4. y = 54x + 3
This equation has a slope of 54 and a y-intercept of 3.
To determine which equation represents the graph, you need to compare the slope and y-intercept values with the information provided in the question. Based on the given information, it is not clear which equation represents the graph.
Please provide more information or a clearer description of the graph to make a more accurate determination.