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 \(\displaystyle \frac{1}{3}\).

Write the formula to find the slope.

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

Either equation will work.  Let's choose the latter.  Substitute the points.

\(\displaystyle m=\frac{y_1-y_2}{x_1-x_2}=\frac{8-(-7)}{5-(-3)}= \frac{15}{8}\)

To find the slope, put the equation in the form of \(\displaystyle y=mx+b\).

\(\displaystyle 2x+3y=-9\)

\(\displaystyle 3y=-2x-9\)

\(\displaystyle y=-\frac{2}{3}x-3\)

Since \(\displaystyle m=-\frac{2}{3}\), that is the value of the slope.

The definition of \(\displaystyle f(x)\) is written in slope-intercept form \(\displaystyle f(x )= mx + b\), in which \(\displaystyle m\), the coefficient of \(\displaystyle x\), is the slope of its line. \(\displaystyle f(x) = 5x - 17\), so the slope of its line is \(\displaystyle m = 5\).

We must select the choice whose line has this slope. The definition of \(\displaystyle g(x)\) in each choice is also written in slope-intercept form, so we select the alternative with \(\displaystyle x\)-coefficient 5; the only such alternative is \(\displaystyle g (x) = 5x - 34\).

The \(\displaystyle y\)-intercept of the graph of a function is the point at which it intersects the \(\displaystyle y\)-axis - that is, at which \(\displaystyle x = 0\). This point is \(\displaystyle \left (0, f(0) \right )\), so evaluate \(\displaystyle f(0)\):

\(\displaystyle f \left ( x\right ) = 2x^{2} - 7x + 5\)

\(\displaystyle f \left (0\right ) = 2 \cdot 0^{2} - 7 \cdot 0 + 5\)

\(\displaystyle f \left (0\right ) = 0- 0 + 5 = 5\)

The \(\displaystyle y\)-intercept is \(\displaystyle \left (0,5 \right )\).

The \(\displaystyle y\)-intercept is the point at which the graph crosses the \(\displaystyle y\)-axis; at this point, the \(\displaystyle x\)-coordinate is 0, so substitute \(\displaystyle 0\) for \(\displaystyle x\) in the equation:

\(\displaystyle y = \frac{1}{x^{2}+ x} + 3\)

\(\displaystyle y = \frac{1}{0^{2}+0} + 3\)

\(\displaystyle y = \frac{1}{0} + 3\)

However, since this expression has 0 in a denominator, it is of undefined value. This means that there is no value of \(\displaystyle x\) paired with \(\displaystyle y\)-coordinate 0, and, subsequently, the graph of the equation has no \(\displaystyle y\)-intercept.

The \(\displaystyle y\)-intercept is the point at which the graph crosses the \(\displaystyle y\)-axis; at this point, the \(\displaystyle x\)-coordinate is 0, so substitute \(\displaystyle 0\) for \(\displaystyle x\) in the equation:

\(\displaystyle y = \frac{3}{\left | 3x-8\right |}\)

\(\displaystyle y = \frac{3}{\left | 3 \cdot 0 -8\right |}\)

\(\displaystyle y = \frac{3}{\left | 0 -8\right |}\)

\(\displaystyle y = \frac{3}{\left | -8\right |}\)

\(\displaystyle y = \frac{3}{ 8}\)

The \(\displaystyle y\)-intercept is \(\displaystyle \left ( 0, \frac{3}{8}\right )\).