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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=8x
y equals 8 x

y=x
y equals x

y=33x
y equals Start Fraction 3 over 3 End Fraction x

y=3x

1 answer

To find the equation of the line in the graph that passes through the origin (0, 0) and the point (8, 8), we can use the general formula for a straight line:

\[ y = mx \]

where \( m \) is the slope of the line.

  1. Calculate the slope (\( m \)):

The slope is calculated by using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

For the points (3, 3) and (8, 8):

  • \( (x_1, y_1) = (3, 3) \)
  • \( (x_2, y_2) = (8, 8) \)

Substituting the values:

\[ m = \frac{8 - 3}{8 - 3} = \frac{5}{5} = 1 \]

  1. Write the equation:

Now substituting \( m \) back into the line equation:

\[ y = 1x \]

which simplifies to:

\[ y = x \]

Therefore, the derived equation of the line through the origin is:

y = x

The correct response is: y=x