To rearrange the equation into a \(\displaystyle y=mx+b\) format, you want to isolate the \(\displaystyle y\) so that it is the sole variable, without a coefficient, on one side of the equation.

First, add \(\displaystyle 11x\) to both sides to get \(\displaystyle 6y=7+16x\) .

Then, divide both sides by 6 to get \(\displaystyle y=\frac{7+16x}{6}\) .

If you divide each part of the numerator by 6, you get \(\displaystyle y=\frac{7}{6}+\frac{16x}{6}\) . This is in a \(\displaystyle y=b+mx\) form, and the \(\displaystyle m\) is equal to \(\displaystyle \frac{16}{6}\), which is reduced down to \(\displaystyle \frac{8}{3}\) for the correct answer.

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

First put the question in slope intercept form (y = mx + b):  

–(1/6)y = –(14/3)x – 7 =>

y = 6(14/3)x – 7

y = 28x – 7.

The slope is 28.

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

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

Use the give points in this formula to calculate the slope.

\(\displaystyle m=\frac{1-2}{3-5}=\frac{-1}{-2}=\frac{1}{2}\)

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

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

Use the give points in this formula to calculate the slope.

\(\displaystyle m=\frac{3-(-4)}{7-8}=\frac{7}{-1}=-7\)

\(\displaystyle 3x + 4y = 22\)

To calculate the slope of a line from an equation of the line, the easiest way to proceed is to solve it for \(\displaystyle y\).  This will put it into the format \(\displaystyle y=mx+b\), making it very easy to find the slope \(\displaystyle m\).  For our equation, it is:

\(\displaystyle 4y = 22-3x\) or \(\displaystyle 4y = -3x+22\)

Next you merely need to divide by \(\displaystyle 4\):

\(\displaystyle y = \frac{-3}{4}x+\frac{22}{4}\)

Thus, the slope is \(\displaystyle \frac{-3}{4}\)

To begin, it is easiest to find the slope of a line by putting it into the form \(\displaystyle y=mx+b\).  \(\displaystyle m\) is the slope, so you can immediately find this once you have the format correct.  Thus, solve our equation for \(\displaystyle y\):

\(\displaystyle 2y = 88-4x\)

\(\displaystyle y = -2x +44\)

Now, recall that perpendicular lines have slopes of opposite sign and reciprocal numerical value.  Thus, if our slope is \(\displaystyle -2\), its perpendicular paired line will have a slope of \(\displaystyle \frac{1}{2}\).

The easiest way to find the slope of a line based on its equation is to put it into the form \(\displaystyle y=mx+b\). In this form, you know that \(\displaystyle m\) is the slope.  

Start with your original equation \(\displaystyle 3x + 5y = y + 20\).

Now, subtract \(\displaystyle y\) from both sides:

\(\displaystyle 3x + 4y = 20\)

Next, subtract \(\displaystyle 3x\) from both sides:

\(\displaystyle 4y = 20-3x\)

Finally, divide by \(\displaystyle 4\):

\(\displaystyle y = 5-\frac{3}{4}x\)

This is the same as:

\(\displaystyle y = -\frac{3}{4}x + 5\)

Thus, the slope is \(\displaystyle -\frac{3}{4}\).

The slope of an equation can be calculated by simplifying the equation to the slope-intercept form \(\displaystyle y = mx + b\), where m=slope.

Since \(\displaystyle 4y - 5 = 12x\), we can solve for y. In shifting the 5 to the other side, we are left with \(\displaystyle 4y = 12x + 5\).

This can be further simplified to 

\(\displaystyle y = 3x + \frac{5}{4}\), leaving us with the \(\displaystyle y = mx + b\) slope intercept form.

In this scenario, \(\displaystyle m=3\), so slope \(\displaystyle =3\).

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.