Question

Given the equation y - 3= 1/2 (x+6) in point-slope form, identify the equation of the same line in slope-intercept form.

Answer 1

$y-3=\dfrac{1}{2}(x+6)\ \ \ \ \ |use\ distributive\ property:a(b+c)=ab+ac\\\\y-3=\dfrac{1}{2}x+3\ \ \ \ |add\ 3\ to\ both\ sides\\\\\boxed{y=\frac{1}{2}x+6}$

Answer 2

Answer:  The correct equation is (C) $y=\dfrac{1}{2}x+6.$

Step-by-step explanation: The given equation is

$y-3=\dfrac{1}{2}(x+6)~~~~~~~~~~~~~~~~~~~~~(i)$

We are to identify the equation of the above line in slope-intercept form.

The equation of a straight line in slope-intercept form is given by

$y=mx+c,$

where 'm' is the slope and 'c' is the y-intercept of the line.

From equation (i), we have

$y-3=\dfrac{1}{2}(x+6)\\\\\\\Rightarrow y-3=\dfrac{1}{2}x+3\\\\\\\Rightarrow y=\dfrac{1}{2}x+3+3\\\\\\\Rightarrow y=\dfrac{1}{2}x+6.$

Here, slope, $m=\dfrac{1}{2}$ and y-intercept, $c=6.$

Therefore, the correct equation is slope-intercept form is

$y=\dfrac{1}{2}x+6.$

Option (C) is correct.