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.

Question

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=3x
y equals 3 x

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

y=x

Answer 1

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

The slope (m) is calculated using the formula:

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

Using the points (3, 3) as \((x_1, y_1)\) and (8, 8) as \((x_2, y_2)\):

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

So, the slope \(m\) is 1. Since the line passes through the origin (0, 0) and we derived that \(m=1\), we can write the equation of the line in slope-intercept form:

\[ y = mx \]

Substituting in the value of \(m\):

\[ y = 1x \]

This simplifies to:

\[ y = x \]

Thus, the correct response is:

y = x