What is the equation of this line?

Question

Responses

y=12x−3
y equals fraction 1 half end fraction x minus 3

y=−12x−3
y equals negative fraction 1 half end fraction x minus 3

y=−2x−3
y equals negative 2 x minus 3

y=2x−3
y equals 2 x minus 3
Number graph ranging from negative 5 to 5 on both the x and y axis. A line passes through the point begin ordered pair 0 comma negative 3 end ordered pair and the point begin ordered pair 4 comma negative 1 end ordered pair

Answer 1

To find the equation of the line that passes through the points (0, -3) and (4, -1), we can first calculate the slope (m) of the line using the formula:

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

Plugging in the coordinates of the given points:

\[ m = \frac{-1 - (-3)}{4 - 0} = \frac{-1 + 3}{4} = \frac{2}{4} = \frac{1}{2} \]

Now that we have the slope \( m = \frac{1}{2} \), we can use the point-slope form of the equation of a line, which is given by:

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

Using one of the points (0, -3):

\[ y - (-3) = \frac{1}{2}(x - 0) \]

This simplifies to:

\[ y + 3 = \frac{1}{2}x \]

Subtracting 3 from both sides:

\[ y = \frac{1}{2}x - 3 \]

Thus, the equation of the line is:

\[ y = \frac{1}{2}x - 3 \]

This corresponds to the response:

y equals fraction 1 half end fraction x minus 3.