Finding Slope and Intercepts

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GED Math › Finding Slope and Intercepts

Questions 11 - 20

What is the slope of the line that passes through the points and ?

$-\frac{1}{8}$

$\frac{7}{8}$

$\frac{1}{8}$

Explanation

Recall how to find the slope of a line:

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

Plug in the coordinates from the given points to find the slope.

$\text{Slope}=\frac{4-5}{12-4}=-\frac{1}{8}$

The slope of the line is $-\frac{1}{8}$ .

A line on the coordinate plane has as its equation .

Which of the following is its slope?

$-\frac{3}{8}$

$\frac{3}{8}$

$\frac{8}{3}$

$-\frac{8}{3}$

Explanation

Rewrite the equation in the slope-intercept form , with the slope, as follows:

Subtract from both sides:

Multiply both sides by $\frac{1}{8}$ , distributing on the right:

$\frac{1}{8} \cdot 8y =\frac{1}{8} \cdot \left ( -3x + 28 \right )$

$y =\frac{1}{8} \cdot ( -3x) +\frac{1}{8} \cdot 28$

$y =\frac{1}{8} \cdot \frac{ -3}{1}\cdot x +\frac{1}{8} \cdot \frac{28}{1}$

$y =- \frac{3}{8} x +\frac{28}{8}$

$y =- \frac{3}{8} x +\frac{7}{2}$

In the slope-intercept form, the coefficient of is the slope . This is $- \frac{3}{8}$ .

Find the slope of a straight line that passes through $\small (1,2)$ and $\small (5,8)$ .

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

$\small m=-\frac{3}{2}$

$\small m=-\frac{2}{3}$

$\small m=\frac{8}{5}$

$\small m=\frac{2}{1}$

Explanation

In order to find the slope, you'll need to use the slop formula, which is $\small m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

Our $\small y_2$ is $\small 8$ , our $\small y_1$ is $\small 2$ , our $\small x_2$ is $\small 5$ and our $\small x_1$ is $\small 1$ .

If you're confused on why I labeled our numbers like this, know that whatever coordinate your given first is your coordinate $\small 1$ and your next coordinate is coordinate $\small 2$ .

In math terms, our coordinates look like this $\small (x_{1},y_{1}) (x_{2},y_{2})$ .

Now that we know what number goes where, it's just a matter of solving the equation for $\small m$ .

$\small m=\frac{8-2}{5-1}$

$\small m=\frac{6}{4}$

Now we could leave our answer like that, but our fraction can actually be reduced even further. See how both the $\small 6$ and the $\small 4$ are divisible by $\small 2$ ? Because they share this $\small 2$ , we can divide both the $\small 6$ and $\small 4$ in order to get the smallest fraction without changing what the fraction stands for.

$\small \frac{\frac{6}{2}}{\frac{4}{2}}=\frac{3}{2}$

If you're confused on why we can do this, pick up a calculator and find out what the decimal equivalent of $\small \frac{6}{4}$ is, then with $\small \frac{3}{2}$ .

Did you get the same answer? That's because $\small \frac{6}{4}$ and $\small \frac{3}{2}$ are the same answer, but $\small \frac{3}{2}$ is just a smaller version of $\small \frac{6}{4}$ . It's the same for if we multiplied $\small \frac{6}{4}$ with $\small 2$ , $\small 3$ , or $\small 4$ . Give it a try when you have the chance!

Our final answer should be $\small m=\frac{3}{2}$

Find the slope of the following equation:

$-\frac{7}{8}$

$\frac{8}{7}$

Explanation

The given equation is already in slope-intercept form.

The represents the coefficient of the slope.

The answer is:

Where do the following equations intercept?

$x=\frac{1}{3}$

$x=-\frac{1}{3}$

Explanation

If we want to find where the equations intercept, you need to set them equal to each other. So,

becomes,

Subtract 1 from both sides to get the variable by itself,

Divide both sides by 3,

$\frac{3x}{3}=\frac{1}{3}$

gives us our final answer of

$x=\frac{1}{3}$

Find the slope and both x and y intercepts of the following linear equation:

$\frac{1}{2}y=-\frac{1}{2}x-17$

$\slope= -1 \y-int= -34 \x-int= -34$

$\slope= -2 \y-int= -17 \x-int= -1$

$\slope= 1 \y-int= -17 \x-int= 34$

$\slope= 2 \y-int= 17 \x-int= 1$

$\slope= -2 \y-int= -34 \x-int= 34$

Explanation

First we need to recognize that the slope intercept formula is

In our equation there is $\frac{1}{2}$ in front of the y, but we need it to have a coefficient of 1 so we need to multiply both sides of the equation by the reciprocal which is $\frac{2}{1}$

$\frac{2}{1}(\frac{1}{2}y)=\frac{2}{1}(-\frac{1}{2}x-34)$

On the left side of the equation the fractions cancel each other out to be 1. On the right side of the equation we distribute the 2/1 to both terms

Now we have our equation in slope intercept form and we can identify the slope as -1 and the y-int as -34.

Next we need to find the x-int which we do by plugging in 0 for y and solving for x

Following order of operations, first we add 34 to both sides

Next we need to divide both sides by -y so that we can solve for x

$\frac{34}{-1}=\frac{-x}{-1}$

Our x-int is -34.

Tip: Don't forget that whenever we see a variable without a coefficient, we know that it has an invisible 1 in front of it, or in this case since there is a negative sign in front of the x, we know that there is an invisible -1

What is the slope of the following equation?