he function g(x) has a slope of −56
. The value of g(x) is 5
when x
is 6
. Explain how the graph of g(x) can be used to find the x
-intercept.(2 points)
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Start at
the point (6, 5) on the graph of g(x). Then, from that point, move in the opposite direction of the slope (-56) by counting the slope units. Continuing this pattern, locate another point on the graph with a y-value of 0. This point represents the x-intercept.
the point (6,5) on the graph of g(x). From this point, we can use the slope of -56 to find the x-intercept.
To find the x-intercept, we need to find the point where the graph intersects the x-axis, which means the y-coordinate would be 0.
Using the slope, we can determine the change in y-coordinate for a given change in x-coordinate. In this case, for every 1 unit increase in x, the y-coordinate would decrease by 56 units.
Starting from the point (6,5), we can find the x-intercept by moving in the opposite direction of the slope. Since the slope is negative, we need to move down and to the left to find the x-intercept.
We can start by subtracting 56 from the y-coordinate:
5 - 56 = -51
This gives us the new y-coordinate of (-51).
Next, we can determine the change in x-coordinate needed to reach the x-intercept. Since the change in y-coordinate is 56 units for every 1 unit change in x-coordinate, we can set up a proportion to solve for the change in x:
Change in x / Change in y = 1 / 56
Solving for the change in x, we get:
Change in x = (Change in y) / (1 / 56) = (-51) / (1 / 56) = -2856
So, starting from the point (6,5), we need to move left by 2856 units to reach the x-intercept.
The x-intercept can be found by subtracting 2856 from the x-coordinate of 6:
6 - 2856 = -2850
Therefore, the x-intercept of the graph of g(x) is -2850.
the point (6,5) on the graph of g(x). The x-intercept is the point where the graph of g(x) intersects the x-axis. In other words, it is the value of x when g(x) is equal to zero.
To find the x-intercept, we can start by using the given information that the slope of g(x) is -56. The slope represents the change in y divided by the change in x. In this case, it means that for every increase of 1 in x, the value of g(x) decreases by 56.
Since the value of g(x) is 5 when x is 6, we can use this information to find the y-intercept (the point where the graph intersects the y-axis). The y-intercept is found by setting x to 0 in the equation of the line. So we have:
g(0) = g(6) - 56(0 - 6)
g(0) = 5 - 56(0 - 6)
g(0) = 5 - 56(-6)
Simplifying this equation gives us:
g(0) = 5 + 336
g(0) = 341
So the y-intercept is (0, 341).
Now we can use this information to find the x-intercept. Since the x-intercept is the point where g(x) is equal to zero, we can set g(x) to zero and solve for x. In other words, we have:
0 = 5 - 56(x - 6)
To solve for x, we can first distribute the -56:
0 = 5 - 56x + 336
Next, we can combine like terms:
56x = 341
Finally, we can divide both sides of the equation by 56 to solve for x:
x = 341/56
So the x-intercept is approximately 6.09.
Therefore, the graph of g(x) can be used to find the x-intercept by analyzing the slope of the function and its y-intercept. By setting g(x) to zero and solving for x, we can determine the x-coordinate of the point where the graph intersects the x-axis.