Which equation represents the graph?

Question

a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 4
y equals negative one third times x minus 1
y = −3x − 1
y equals negative one third times x plus one third
y equals negative 3 times x plus one third

Answer 1

To determine the equation that represents the graph passing through the points (0, -1) and (1, -4), we can start by finding the slope of the line.

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

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

Plugging in the points (0, -1) and (1, -4):

\[ m = \frac{-4 - (-1)}{1 - 0} = \frac{-4 + 1}{1} = \frac{-3}{1} = -3 \]

Now 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 the point (0, -1):

\[ y - (-1) = -3(x - 0) \]

This simplifies to:

\[ y + 1 = -3x \quad \Rightarrow \quad y = -3x - 1 \]

Now, we compare this with the given options. The correct equation that represents the graph is:

y = −3x − 1.