Question

find the equation of a line that passes (2, 4) with slope 1/2

Answer 1

To find the equation of a line that passes through the point (2, 4) with a slope of \( \frac{1}{2} \), you can use the point-slope form of the equation of a line, which is given by:

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

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

Plugging in the values:
- \( m = \frac{1}{2} \)
- \( (x_1, y_1) = (2, 4) \)

The equation becomes:

\[
y - 4 = \frac{1}{2}(x - 2)
\]

Now, distribute the slope on the right side:

\[
y - 4 = \frac{1}{2}x - 1
\]

Next, add 4 to both sides to solve for \( y \):

\[
y = \frac{1}{2}x - 1 + 4
\]
\[
y = \frac{1}{2}x + 3
\]

Thus, the equation of the line in slope-intercept form is:

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