Questions: Which linear function represents the line given by the point-slope equation y-8=1/2(x-4) ? f(x)=1/2 x+4 f(x)=1/2 x+6 f(x)=1/2 x-10 f(x)=1/2 x-12

Transcript text: Which linear function represents the line given by the point-slope equation $y-8=\frac{1}{2}(x-4)$ ? $f(x)=\frac{1}{2} x+4$ $f(x)=\frac{1}{2} x+6$ $f(x)=\frac{1}{2} x-10$ $f(x)=\frac{1}{2} x-12$

Solution

Solution Steps

Step 1: Rewrite the point-slope equation in slope-intercept form

Start with the given point-slope equation: \[ y - 8 = \frac{1}{2}(x - 4) \] Distribute the slope $ \frac{1}{2} $ on the right-hand side: \[ y - 8 = \frac{1}{2}x - 2 \]

Step 2: Solve for $ y $

Add 8 to both sides of the equation to isolate $ y $: \[ y = \frac{1}{2}x - 2 + 8 \] Simplify the constants: \[ y = \frac{1}{2}x + 6 \]

Step 3: Compare with the given options

The equation $ y = \frac{1}{2}x + 6 $ matches the second option: \[ f(x) = \frac{1}{2}x + 6 \]