Linear Algebra - GED Math

Card 0 of 730

Rewrite the given equation in slope-intercept form.

Tap to see back →

The slope-intercept format is:

Add on both sides.

Subtract 6 from both sides.

Divide by 3 on both sides.

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

The answer is:

Rewrite the following equation to slope-intercept format:

Tap to see back →

The slope intercept form of a line is:

Subtract from both sides.

Divide by 9 on both sides.

$\frac{9y }{9}$= $\frac{-2x+31}{9}$

The answer is: $y= -$\frac{2}{9}$x+\frac{31}{9}$$

Find the slope and y-intercept of the line depicted by the equation:
$\small y=-$\frac{1}{3}$x+7$

Tap to see back →

The equation is written in slope-intercept form, which is:
$\small y=mx+b$

where is equal to the slope and is equal to the y-intercept. Therefore, a line depicted by the equation

$\small y=-$\frac{1}{3}$x+7$

has a slope that is equal to $-$\frac{1}{3}$$ and a y-intercept that is equal to .

Find the slope and y-intercept of the line that is represented by the equation $y=\frac{2}{3}$x-8$

Tap to see back →

The slope-intercept form of a line is: , where is the slope and is the y-intercept.

In this equation, $m \textup{ = }$\frac{2}{3}$$ and $y \textup{ = }-8$

What is the slope and y-intercept of the following line?

Tap to see back →

Convert the equation into slope-intercept form, which is , where is the slope and is the y-intercept.

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

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

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

Refer to above red line. What is its slope?

Tap to see back →

Given two points, , the slope can be calculated using the following formula:

$m = $$\frac{y_{2}$$$-y_{1}$$}{x_{2}$-x _{1}}$

Set :

$m = $\frac{8-0}{0-(-4)}$ = $\frac{8}{4}$ = 2$

The grade of a road is defined as the slope of the road expressed as a percent as opposed to a fraction or decimal.

A road is graded so that for every 40 feet of horizontal distance, the road rises 6 feet. What is the grade of the road?

Tap to see back →

The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is $\frac{6}{40}$ . Multiply this by 100% to get its equivalent percent:

$$\frac{6}{40}$ \times 100 % = 15 %$

This is the correct choice.

What is the slope of the line perpendicular to ?

Tap to see back →

In order to find the perpendicular of a given slope, you need that given slope! This is easy to compute, given your equation. Just get it into slope-intercept form. Recall that it is

Simplifying your equation, you get:

$y=\frac{-1}{2}$x+\frac{93}{6}$$

This means that your perpendicular slope (which is opposite and reciprocal) will be .

What is the equation of a line with a slope perpendicular to the line passing through the points and ?

Tap to see back →

First, you should solve for the slope of the line passing through your two points. Recall that the equation for finding the slope between two points is:

$\frac{rise}{run}$ = $\frac{y_2-y_1}{x_2-x1}$

For your data, this is

$$\frac{19-4}{7-2}$=\frac{15}{5}$=3$

Now, recall that perpendicular slopes are opposite and reciprocal. Therefore, the slope of your line will be $\frac{-1}{3}$ . Given that all of your options are in slope-intercept form, this is somewhat easy. Remember that slope-intercept form is:

is your slope. Therefore, you are looking for an equation with $m=\frac{-1}{3}$$

The only option that matches this is:

$y=\frac{-1}{3}$x+94$

What is the x-intercept of ?

Tap to see back →

Remember, to find the x-intercept, you need to set equal to zero. Therefore, you get:

Simply solving, this is

Find the slope of the line that has the equation:

Tap to see back →

Step 1: Move x and y to opposite sides...

We will subtract 2x from both sides...

Result,

Step 2: Recall the basic equation of a line...

, where the coefficient of y is .

Step 3: Divide every term by to change the coefficient of y to :

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

Step 4: Reduce...

$y=\frac {2}{3}x+\frac {4}{3}$

Step 5: The slope of a line is the coefficient in front of the x term...

So, the slope is $\frac {2}{3}$

Find the slope of the following equation:

Tap to see back →

In order to find the slope, we will need the equation in slope-intercept form.

Distribute the negative nine through the binomial.

The slope is:

What is the y-intercept of the following equation?

Tap to see back →

The y-intercept is the value of when .

Substitute the value of zero into , and solve for .

Subtract 7 from both sides.

The answer is:

Find the slope and y-intercept, respectively, given the following equation:

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

Tap to see back →

Rewrite the equation in slope-intercept format:

Divide by negative two on both sides. This is also the same as multiplying both sides by negative half.

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

$y = $\frac{1}{3}$+\frac{1}{2}$x$

Rearrange the terms.

$y =\frac{1}{2}$x+ $\frac{1}{3}$$

The slope is: $\frac{1}{2}$

The y-intercept is: $\frac{1}{3}$

The answer is: $\frac{1}{2}$, $\frac{1}{3}$

Find the slope of the following function:

Tap to see back →

Simplify the terms of the equation by distribution.

Subtract the terms.

The equation is now in slope-intercept form, where .

The slope is .

The answer is .

Rewrite the following equation in slope-intercept form:

Tap to see back →

The slope-intercept form of a line is:

Subtract from both sides.

Simplify both sides.

Divide by negative nine on both sides.

$\frac{-9y}{-9}$= $\frac{-2x-1}{-9}$

The equation is: $y=\frac{2}{9}$x +\frac{1}{9}$$

What is the slope of the following equation?

Tap to see back →

To determine the slope, we will need the equation in slope-intercept form.

Subtract on both sides.

Divide by 9 on both sides.

$\frac{9y }{9}$= $\frac{-x-7}{9}$

Split both terms on the right side.

$y= -$\frac{1}{9}$x-$\frac{7}{9}$$

The slope is: $-$\frac{1}{9}$$

Identify the y-intercept:

Tap to see back →

In order to find the y-intercept, we will need to let and solve for .

Subtract from both sides. Do NOT divide by on both sides.

The answer is:

What is the x-intercept of the following equation?

Tap to see back →

In order to find the x-intercept, we will need to let , and solve for .

Add on both sides.

Divide by five on both sides.

$\frac{5x}{5}$=\frac{3}{5}$

The answer is: $\frac{3}{5}$

A line on the coordinate plane has as its equation .

Which of the following is its slope?

Tap to see back →

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}$$ .