If the graph of the y=5x-4 is up 3 units, we will find which of the given statements is true. Before examining the statements, let's plot the graph of our function. To do so we will first write the function in .
y=5x-4 ⇒ y= 5x+( - 4)
In this function 5 is the and - 4 is the . We will now plot the y-intercept and then use the slope by moving 5 units in the positive vertical direction when we move 1 unit in the positive horizontal direction to plot another point. Then we will connect the points with a line.
Notice that the y-intercept of the resulting line is - 1, whereas it has the same slope as the graph of y=5x-4.
y= 5x+( - 1) ⇒ y=5x-1
We can now examine each statement given in the options one by one.
Option F
Let's first examine the given statement.
|
The resulting line will have a slope that is greater than the slope of the graph of y=5x-4.
|
From the graph, we can observe that the original function and the resulting function have the same slope, which is 5.
Therefore, the statement in option F is false. The slope of the resulting line is not greater than the slope of the graph of the original function.
Option G
In this option, we are given a statement comparing the of the original function and the resulting function.
|
The resulting line will have the same x-intercept as the graph of y=5x-4.
|
Recall that x-intercept is the point where a graph intercept the x-axis. In other words, it is the x-value where y=0.
As we can see, the x-intercepts of the graphs are not the same. The x-intercept of the graph of y=5x-4 is x=0.8, whereas the x-intercept of the resulting line is x=0.2. Therefore, the statement in option G is false.
Option H
Let's examine the given statement.
|
The resulting line will be parallel to the graph of y=5x-4.
|
Recall that two lines are if and only if their slopes are equal. In Option F, we have already showed that the original function and the resulting function have the same slope, which implies that the graphs of these two functions are parallel.
Therefore, the statement in option H is true.
Option I
Finally, we will examine the statement given in option I.
|
The resulting line will have a slope of - 1.
|
When examining the statement in option F we found that the slope of the resulting line is 5. Therefore, the statement in option I is false.
