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.

x − 2y = −12

y= 1/2x

y=1/2x+6

y=1/2x+9

Answer 1

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

Answer 2

Answer: The correct equation is (C)
`y=(1)/(2)x+6.`

Step-by-step explanation: The given equation is

`y-3=(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=(1)/(2)(x+6)\\\\\\\Rightarrow y-3=(1)/(2)x+3\\\\\\\Rightarrow y=(1)/(2)x+3+3\\\\\\\Rightarrow y=(1)/(2)x+6.`

Here, slope,
`m=(1)/(2)` and y-intercept,
`c=6.`

Therefore, the correct equation is slope-intercept form is

`y=(1)/(2)x+6.`

Option (C) is correct.