Question

What is the equation of this line?

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.**