Graphing Proportional Relationships Quick Check
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Question
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line line passes through points plotted at left parenthesis 3 comma 3 right parenthesis and left parenthesis 8 comma 8 right parenthesis.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=3x
y equals 3 x
y=x
y equals x
y=8x
y equals 8 x
y=33x
The correct answer is y=x.
are u sure
To find the equation of a line through the origin on the given graph, we need to determine the slope (m) of the line.
The slope (m) can be found using the formula:
m = (change in y) / (change in x)
From the given points on the line (3, 3) and (8, 8), the change in y is 8 - 3 = 5, and the change in x is 8 - 3 = 5.
Therefore, the slope (m) is 5/5, which simplifies to 1.
Since the line passes through the origin, the y-intercept (b) is 0.
Putting these values into the equation y = mx + b, we get:
y = 1x + 0
Simplifying, y = x.
Therefore, the correct equation for the line through the origin on the given graph is:
y = x.
To derive the equation y = mx for a line through the origin using the given graph, you need to calculate the slope of the line. The slope (m) can be found by determining the change in y divided by the change in x between any two points on the line.
In this case, you are given two points on the line: (3, 3) and (8, 8). The change in y is 8 - 3 = 5, and the change in x is also 8 - 3 = 5. Therefore, the slope (m) is 5/5 = 1.
Since the line passes through the origin (0, 0), the equation takes the form y = mx, where m is the slope. Therefore, the equation for the line is y = 1x, or simply y = x.
Hence, the correct answer is y = x.