The formula to find slope and y-intercept is:

$\displaystyle y=mx +b$

$\displaystyle m=\frac{1}{6}$ and $\displaystyle b =-\frac{1}{2}$

The formula to find slope and y-intercept is:

$\displaystyle y=mx +b$

$\displaystyle y = 3x+2x-1$

Combine like terms.

$\displaystyle y = 5x -1$

$\displaystyle m=5$ and $\displaystyle b = -1$

slope   = $\displaystyle \frac{rise}{run}$

rise  =   changes in y 

run  =   changes in x

$\displaystyle x$     $\displaystyle -2,0,2,4$

$\displaystyle y$       $\displaystyle 8, 5, 2, -1$

The change in the $\displaystyle y$ coordinates is that the numbers are decreasing by 3 or -3.

The change in the $\displaystyle x$ coordinates is that the numbers are increasing by 2 or +2;

slope = $\displaystyle \frac{-3}{2}$

 slope  = $\displaystyle \frac{rise}{run}$

rise  =   changes in y 

run  =   changes in x

$\displaystyle x$     $\displaystyle -8,-4,0,4$

$\displaystyle y$       $\displaystyle 2, 5, 8, 11$

The change in the $\displaystyle y$ coordinates is that the numbers are increasing by 3 or +3.

The change in the $\displaystyle x$ coordinates is that the numbers are increasing by 4 or +4.

slope = $\displaystyle \frac{3}{4}$

slope =  $\displaystyle \frac{rise}{run}$

rise  =   changes in y 

run  =   changes in x

$\displaystyle x$        $\displaystyle -6,-4,-2,0$

$\displaystyle y$       $\displaystyle -3, -3, -3, -3$

There is zero change in the $\displaystyle y$ coordinates.

The change in the $\displaystyle x$ coordinates is that the numbers are increasing by 2 or +2.

slope = $\displaystyle \frac{0}{2}$

$\displaystyle m = 0$

If the $\displaystyle y$  coordinates are the same, then it will be a horizontal line.  The slope of a horizontal line is 0.

The formula for slope is:

$\displaystyle m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$\displaystyle m = \frac{5-(-1)}{6-3}$

$\displaystyle m = \frac{5+1}{6-3}$

$\displaystyle m = \frac{6}{3}$

$\displaystyle m=2$

The formula for slope is:

$\displaystyle m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$\displaystyle m = \frac{-8-2}{6-1}$

$\displaystyle m = \frac{-10}{5}$

$\displaystyle m=-2$

The formula for slope is:

$\displaystyle m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$\displaystyle m= \frac{-2-(-1)}{-2- (-3)}$

$\displaystyle m = \frac{-2+1}{-2+3}$

$\displaystyle m=\frac{-1}{1}$

$\displaystyle m=1$

Step 1: The current equation is in standard form, where x and y are both on one side of the equal sign..

Step 2: Change the equation to slope-intercept form.. Move the y to the other side

$\displaystyle 3x=6y-14$

Step 3: Move the constant to the other side:

$\displaystyle 3x+14=6y$

Step 4: Divide by the coefficient in front of $\displaystyle y$:

$\displaystyle \frac {3x+14}{6}=\frac {6y}{6}$

Step 5: Split the left side into two fractions and simplify:

$\displaystyle \frac {3x}{6}+\frac {14}{6}=y$

$\displaystyle \rightarrow \frac {1}{2}x+\frac {7}{3}=y$

Step 6. Locate the slope. The slope is the coefficient of the x term.

The slope is $\displaystyle \frac {1}{2}$, or $\displaystyle m=\frac {1}{2}$

Step 1: Subtract $\displaystyle x$ from both sides:

$\displaystyle x-x+4y=-x+12 \implies 4y=-x+12$

Step 2: Divide by the coefficient of the y term..In this case, divide by $\displaystyle 4$.

$\displaystyle \frac {4y}{y}=\frac {-x+12}{4}$

Simplify and separate fraction on right side:

$\displaystyle y=-\frac{x}{4}+\frac {12}{4}\implies y=-\frac {1}{4}x+3$

Step 3: Locate the y-intercept (also known as b):

If we compare our equation to the general slope-intercept form: $\displaystyle y=mx+b$, we see that $\displaystyle 3=b$..

The value of $\displaystyle b$ is $\displaystyle 3$.