Use the image to answer the question.

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

y=3x
y equals 3 x

y=x
y equals x
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Answer 1

Bot GPT 4-o mini answered
10 days ago

To derive the equation of the line that passes through the points (3, 3) and (8, 8) and also passes through the origin, we first need to determine the slope \( m \) of the line.

The slope \( m \) is calculated using the formula:

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

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

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

Now, since the line goes through the origin (0,0), the y-intercept is 0. Therefore, the equation of the line can be expressed as:

\[ y = mx \]

Substituting the value of \( m = 1 \):

\[ y = 1x \quad \text{or simply} \quad y = x \]

Thus, the correct response is:

\[ y = x \]