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).