Question

Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds
y = one-third x + 1

Answer 1

To find the equation of a line with a slope of \(\frac{1}{3}\) that passes through the point \((-2, 1)\), we can use the point-slope formula:

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

where \(m\) is the slope, and \((x_1, y_1)\) is the point the line passes through. In this case, \(m = \frac{1}{3}\), \(x_1 = -2\), and \(y_1 = 1\).

Plugging these values into the formula gives:

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

Now, simplify the equation:

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

Adding \(1\) (or \(\frac{3}{3}\)) to both sides results in:

\[
y = \frac{1}{3}x + \frac{2}{3} + \frac{3}{3}
\]
\[
y = \frac{1}{3}x + \frac{5}{3}
\]

Therefore, the equation of the line is:

\[
y = \frac{1}{3}x + \frac{5}{3}
\]

The correct answer is:

**y = one-third x + five-thirds**.