Question

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(3,4), m=\frac{1}{2}$$

Short answer

The equation of the line that passes through the point (3,4) and has given slope \(\frac{1}{2}\) written in slope-intercept form is \(y = \frac{1}{2}x + \frac{5}{2}\).

Step-by-step solution

Insert the given values into the formula

The slope-intercept form is \(y = mx + b\), here \(x = 3, y = 4\) and the slope (\(m\)) is \(\frac{1}{2}\). Insert these values into the equation: \(4 = \frac{1}{2}(3) + b\).

Solve for \(b\)

Now we will solve the equation for \(b\), the y-intercept. First, simplify the right side \(4 = \frac{3}{2} + b\), and then subtract \(\frac{3}{2}\) from both sides to isolate \(b\): \(b = 4 - \frac{3}{2} = \frac{5}{2}\).

Write the final equation

Now that we have the slope (\(m\)) and the y-intercept (\(b\)), we can write the final equation of the line: \(y = \frac{1}{2}x + \frac{5}{2}\).