Step-by-step explanation:
With the point-slope formula for a line, given the point \((2, 4)\) and a slope of \( \frac{1}{2} \), the equation of the line can be expressed as:
\[ y - y_1 = m(x - x_1) \]
Given:
- Point \((2, 4)\) where \(x_1 = 2\) and \(y_1 = 4\)
- Slope \(m = \frac{1}{2}\)
Substitute these values into the point-slope formula:
\[ y - 4 = \frac{1}{2}(x - 2) \]
Now, simplify this equation to find the equation of the line in slope-intercept form (\(y = mx + b\)) or any other desired form.
The equation of a line with slope-intercept form (\(y = mx + b\)) is found using the point-slope formula \(y - y_1 = m(x - x_1)\). Given the point \((2, 4)\) and a slope of \(1/2\):
First, plug in the values:
\[y - 4 = \frac{1}{2}(x - 2)\]
Let's simplify this equation to get it in slope-intercept form:
\[y - 4 = \frac{1}{2}x - 1\]
\[y = \frac{1}{2}x + 3\]
Therefore, the equation of the line that goes through the point \((2, 4)\) with a slope of \(1/2\) is \(y = \frac{1}{2}x + 3\).
