Question

Which equation represents a line that passes through (–2, 4) and has a slope of StartFraction 2 Over 5 EndFraction.?

Answer 1

To find the equation of a line with a given slope and a point, we can use the point-slope form of the equation of a line, which is:

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

where \((x_1, y_1)\) is the point the line passes through, and \(m\) is the slope.

Given the point \((-2, 4)\) and the slope \(m = \frac{2}{5}\), we can substitute these values into the equation:

1. Set \(x_1 = -2\) and \(y_1 = 4\):
\[
y - 4 = \frac{2}{5}(x - (-2))
\]

2. This simplifies to:
\[
y - 4 = \frac{2}{5}(x + 2)
\]

3. Distributing the slope:
\[
y - 4 = \frac{2}{5}x + \frac{4}{5}
\]

4. Now, add 4 (or \( \frac{20}{5}\)) to both sides to isolate \(y\):
\[
y = \frac{2}{5}x + \frac{4}{5} + \frac{20}{5}
\]
\[
y = \frac{2}{5}x + \frac{24}{5}
\]

Therefore, the equation of the line that passes through \((-2, 4)\) with a slope of \(\frac{2}{5}\) is:

\[
y = \frac{2}{5}x + \frac{24}{5}
\]