A line intersects the graph of y= x^2 twice. One point has an x- coordinate of -4, and the other point has an x-coordinate of 2.
A) Draw a sketch of both graphs, and find the equation of the line.
B) Find the measure of the angle that the line makes with the x-axis.
A) To draw a sketch of both graphs, start by plotting the two given points (-4, y1) and (2, y2) on the graph.
For the first point, when the x-coordinate is -4, substituting it into the equation y = x^2, we get y1 = (-4)^2 = 16. So the first point is (-4, 16).
For the second point, when the x-coordinate is 2, substituting it into the equation y = x^2, we get y2 = (2)^2 = 4. So the second point is (2, 4).
Now, plot these two points on the graph.
Next, connect the two points with a straight line. This line will be the line that intersects the graph of y = x^2 twice.
B) To find the measure of the angle that the line makes with the x-axis, we need to determine the slope of the line. The slope of a line is given by the formula:
slope = (change in y) / (change in x)
In this case, the change in y is y2 - y1 = 4 - 16 = -12, and the change in x is 2 - (-4) = 6.
Therefore, the slope of the line is -12/6 = -2.
The line makes an angle with the x-axis, which can be found using the inverse tangent function. The inverse tangent of the slope will give us the angle in radians. We can then convert radians to degrees if desired.
So, to find the measure of the angle that the line makes with the x-axis, we can use the formula:
angle = arctan(slope)
angle = arctan(-2)
Using a calculator, we find that the angle is approximately -63.43 degrees, which means the line makes an angle of -63.43 degrees with the x-axis.
I did this question on Monday
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