Question

What is the slope and y-intercept of the equation 3(y − 2) + 6(x + 1) − 2 = 0? A. slope = -2, y-intercept = B. slope = 2, y-intercept = C. slope = -2, y-intercept = D. slope = 2, y-intercept = E. slope = -2, y-intercept =

Answer 1

The correct answer is that the slope is equal to -2 and the y-intercept is equal to 2/3.

To find this, follow the order of operations and solve for y.

3(y − 2) + 6(x + 1) − 2 = 0 ----> distribute

3y - 6 + 6x + 6 - 2 = 0 -----> combine like terms

3y + 6x - 2 = 0 -----> subtract 6x

3y - 2 = -6x -----> add 2

3y = -6x + 2 -----> divide by 3

y = -2x + 2/3

Now we can find the slope as the coefficient of x (-2) and the intercept as the constant (2/3)

Answer 2

Answer:  The slope of the given line is -2 and y-intercept is $\dfrac{2}{3}.$

Step-by-step explanation:  We are given to find the slope and y-intercept of the following equation of a line:

$3(y-2)+6(x+1)-2=0~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the slope-intercept form of the equation of a line 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

$3(y-2)+6(x+1)-2=0\\\\\Rightarrow 3y-6+6x+6-2=0\\\\\Rightarrow 3y+6x=2\\\\\Rightarrow 3y=-6x+2\\\\\Rightarrow y=-2+\dfrac{2}{3}.$

Thus, the slope of the given line is -2 and y-intercept is $\dfrac{2}{3}.$