We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4x + 3y = 7.

Isolate the y term: 3y = 7 – 4x

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

The equation for slope is $\displaystyle \frac{(y_2-y_1)}{(x_2-x_1)}$. You plug in the coordinates from the points given you, and get $\displaystyle \frac{(4-2)}{(3-6)}$, giving you $\displaystyle \frac{2}{-3}$. Note that it does not matter which point you use as point 1 and point 2, as long as you are consistent.

$\displaystyle \frac{(y_2-y_1)}{(x_2-x_1)}$

(6,2) = (x₁,y₁)

(3,4) = (x₂,y₂)

$\displaystyle \frac{(4-2)}{(3-6)}=\frac{2}{-3}=-\frac{2}{3}$

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

To find the slope of a line you must first assign variables to each point. It does not matter which points get which variables as long as you keep the $\displaystyle x_{1}$ and $\displaystyle y_{1}$ and $\displaystyle x_{2}$ and $\displaystyle y_{2}$ consistent when you plug them into the equation.

Then we plug in the variables to this equation where $\displaystyle m$ represents the slope.$\displaystyle m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

Then we plug in our points for $\displaystyle x_{1},x_{2},y_{1},and\ y_{2}$ and the example looks like$\displaystyle m=\frac{(32-12)}{(91-7)}$

Then we perform the necessary subtraction and division to find an answer of $\displaystyle m=\frac{20}{84}=\frac{5}{21}$

$\displaystyle \textup{To find the slope, put the equation into }y=mx+b\textup{ format.}$

$\displaystyle 3y-4x=13$

$\displaystyle 3y=4x+13$

$\displaystyle y = \frac{4}{3}x+\frac{13}{3}\;\;\;\;\;\;\textup{slope}=m = \frac{4}{3}$

Slope intercept form is $\displaystyle y=mx+b$, where $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept.

$\displaystyle y=-x+4$ is the correct answer. The line has a slope of $\displaystyle -1$ and a y-intercept equal to $\displaystyle 4$.

$\displaystyle m=slope=\frac{\Delta y}{\Delta x}=\frac{\left ( y_{2}-y_{1}\right )}{\left ( x_{2}-x_{1}\right )}=$

$\displaystyle \frac{\left ( 6-2\right )}{\left ( 4-1\right )}=\frac{4}{3}$

Solve the equation for $\displaystyle y=mx+b$

where $\displaystyle m$ is the slope of the line:

$\displaystyle 5x+25y=14$

$\displaystyle 25y=-5x+14$

$\displaystyle y=-\left ( \frac{5}{25} \right )x+\frac{14}{25}=-\left ( \frac{1}{5} \right )x+\frac{14}{25}$

$\displaystyle Slope=-\frac{1}{5}$

The slope is the rise over the run.  The line drops in $\displaystyle y$-coordinates by 13 while gaining 5 in the $\displaystyle x$-coordinates.

You can rearrange $\displaystyle 2y-4x=12$ to get an equation resembling the $\displaystyle y=mx+b$ formula by isolating the $\displaystyle y$. This gives you the equation $\displaystyle y=2x+6$. The slope of the equation is 2 (the $\displaystyle m$ within the $\displaystyle y=mx+b$ equation).