Which equation represents the line that passes through points (0, 6) and (2, 0)?

Question

y = negative one-third x + 2
y = negative one-third x + 6
y = negative 3 x + 2
y = negative 3 x + 6

Answer 1

To find the equation of the line that passes through the points (0, 6) and (2, 0), we first need to calculate the slope \( m \) of the line using the formula:

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

Here, \( (x_1, y_1) = (0, 6) \) and \( (x_2, y_2) = (2, 0) \).

Calculating the slope:

\[ m = \frac{0 - 6}{2 - 0} = \frac{-6}{2} = -3 \]

Now that we have the slope, \( m = -3 \), we can use the point-slope form of the equation of a line, which is:

\[ y - y_1 = m(x - x_1) \]

Using point (0, 6):

\[ y - 6 = -3(x - 0) \]

Simplifying this equation:

\[ y - 6 = -3x \] \[ y = -3x + 6 \]

So, the equation of the line that passes through the points (0, 6) and (2, 0) is:

\[ y = -3x + 6 \]

Thus, the correct choice is:

y = negative 3 x + 6.