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The function h is defined by h(x) = -1/4x - 2. Which is the graph of y (March 2021 U.S.)
The function h is defined by h(x) = -1/4x - 2.
Which is the graph of y = h(x)?
Solution
Correct answer: Letter D.
The function defined by h(x) = x - 2 is a linear function, and its graph is a straight line. The slope of the function is 1, which means that for every 1 position you move up, you must also move 1 position to the right. The y-intercept of the function is -2, which means that the line intersects the y-axis at the point (0, -2).
To graph the function, we can follow these steps:
Plot the point (0, -2).
Since the slope is 1 and positive, move up 1 unit and to the right 1 unit. This will land you at the point (1, -1).
Connect these two points with a straight line.
This line will be the graph of the function.
However, the question also asks us to find the equation of the line. To do this, we can use the point-slope form of linear equations:
y - y1 = m(x - x1)
where:
m is the slope of the line
(x1, y1) is a point on the line
In this case, we know that the slope of the line is 1 and that the point (0, -2) is on the line. Plugging these values into the equation, we get:
y - (-2) = 1(x - 0)
Simplifying, we get:
y + 2 = x
This is the equation of the line.
Therefore, the correct answer to the question is letter D, which is the equation y + 2 = x.
Exam Edition: March 2021 U.S.
Exam Year: 2021
Related topics: Algebra, Geometry, Linear Functions