Ask a New Question
Menu

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

y=8x
y equals 8 x

y=3x
y equals 3 x

y=x
y equals x
Skip to navigation

1 answer

To derive the equation of the line in the form \( y = mx \) that goes through the origin and has the same slope as the given line, we first need to determine the slope of the line that passes through the points (3, 3) and (8, 8).

The slope \( m \) can be calculated with the formula:

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

Substituting the values of the two points (3, 3) and (8, 8):

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

We have:

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

Now that we have the slope \( m = 1 \), we can use it to form the equation of the line through the origin:

\[ y = mx = 1x = x \]

Thus, the simplified equation is \( y = x \).

The correct response is: y = x