The least integer function, or celing function, $\displaystyle f(x) = \left \lceil x\right \rceil$, pairs each value of $\displaystyle x$ with the least integer greater than or equal to $\displaystyle x$. Its graph is below.

The given graph is the above graph shifted upward four units. The graph of any function $\displaystyle y = f(x)$ shifted upward four units is $\displaystyle y = f(x) + 4$, so the given graph corresponds to equation $\displaystyle y = \left \lceil x\right \rceil+ 4$.

The graph below is the graph of the absolute value function $\displaystyle f(x)= |x|$, which pairs each $\displaystyle x$-coordinate with its absolute value.

The given graph is the above graph shifted upward five units. The graph of any function $\displaystyle y = f(x)$ shifted upward five units is $\displaystyle y = f(x)+5$, so the correct response is $\displaystyle y = |x| + 5$.

Use the following formula to find the slope:

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values from the points given, we get the following slope:

$\displaystyle \text{Slope}=\frac{1-4}{-5-(-1)}=\frac{-3}{-4}=\frac{3}{4}$

To find the slope of the line that passes through the given points, you can use the slope equation.

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle \text{Slope}=\frac{-1-2}{-2-17}=\frac{-3}{-19}=\frac{3}{19}$

To find the slope of the line that passes through the given points, you can use the slope equation.

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle \text{Slope}=\frac{3-b}{2-a}$

You need to put the equation in $\displaystyle y=mx+b$ form before you can easily find out its slope.

$\displaystyle 5x-9y=12$

$\displaystyle -9y=-5x+12$

$\displaystyle y=\frac{5}{9}x-\frac{4}{3}$

Since $\displaystyle m=\frac{5}{9}$, that must be the slope.

Even though there are variables involved in the coordinates of these points, you can still use the slope formula to figure out the slope of the line that connects them.

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle \text{Slope}=\frac{-9s-8s}{2t-4t}=\frac{-17s}{-2t}=\frac{17s}{2t}$

To find the slope, you will need to put the equation in $\displaystyle y=mx+b$ form. The value of $\displaystyle m$ will be the slope.

$\displaystyle 12x-8y=6$

Subtract $\displaystyle 6$ from either side:

$\displaystyle 8y=12x-6$

Divide each side by $\displaystyle 8$:

$\displaystyle y=\frac{3}{2}x-\frac{3}{4}$

You can now easily identify the value of $\displaystyle m$.

$\displaystyle m=\frac{3}{2}$

You can use the slope formula to figure out the slope of the line that connects these two points. Just substitute the specified coordinates into the equation and then subtract:

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle \text{Slope}=\frac{3-1}{0-8}=\frac{2}{-8}=-\frac{1}{4}$

Rewrite the equation in slope-intercept form, $\displaystyle y=mx+b$.

$\displaystyle 2x-6y=3$

$\displaystyle 2x=3+6y$

$\displaystyle 2x-3=6y$

$\displaystyle \frac{2x-3}{6}=y$

$\displaystyle y=\frac{1}{3}x-\frac{1}{2}$

The slope is the $\displaystyle m$ term, which is $\displaystyle \frac{1}{3}$.