My Good Friend Slope Trivia Quiz

Answer: m

Slope thanks you if you got this correct! How is he supposed to do anything if he doesn't know that he is represented by an "m" in a linear equation? The "b" is the y-intercept, which is where the line crosses the y-axis on a graph. "x" and "y" are just variables; the "y" depends on what you plug in for "x" and, therefore, is known as the dependent variable.

Answer: y = -x + 2

Slope feels ashamed for not knowing this! When his memory came back, he told me to tell you that this is correct because it is in "y = mx + b" form. x + y = -1 is not an accurate answer because it is in "standard form". In order to change y - 4 = 3x to slope-intercept form, you have to add four to both sides. Slope-intercept form for the equation 2x - y + 6 = 0 is obtained by doing this:
2x - y + 6 = 0
-2x -2x
- y + 6 = -2x
- 6 - 6
-y = -2x - 6
Divide each term by a -1.
y = 2x + 6

Answer: 2

Slope thanks you again for helping him get out of that jam! For those who are ignorant of Algebra, Slope wants you to know that whenever a linear equation is in slope-intercept form, whatever number is in front of the independent variable "x" is the slope, or "m".

Answer: -1/4

Whew! In order to find Slope in this equation, you must first put the equation in standard form. You may ask: isn't it already in standard form? The answer Slope told me to give you is that the coefficent (number multiplied "x" times) must be a whole number before an equation is in standard form. To make 1/2 a whole number, you must multiply through the whole equation by two. Now the equation is x + 4y = 6. There are now two ways to obtain the number for slope. The first is to subtract x from both sides, like so:
x + 4y = 6
-x -x
4y = 6 - x
Now, divide all terms by 4 change the equation to slope-intercept form.
y = -1/4x + 3/2
Therefore, Slope is -1/4 in this equation.
Another name for standard form is Ax + By = C form.
To obtain the slope for an equation while it is in standard form, use the formula -A/B.
In our equation, A is 1 and B is 4
-A/B = -1/4
Once again, Slope is -1/4

Answer: 3

Parallel means same slope. Therefore, the equation Slope is in has the same slope as the given equation. To find the slope of 3x - y = 7, first subtract 3x from both sides.
3x - y = 7
-3x -3x
-y = 7 - 3x
Divide all terms by a -1 and switch the term with the variable around with the term lacking a variable to put in slope-intercept form.
y = 3x - 7
The slope is 3.
Slope is in an equation with the same slope as this one.
Slope is 3.

Answer: 3/4

Perpendicular means to take the opposite reciprocal of the slope of a line. First, let's put the equation in slope-intercept form:
4x + 3y = 9
-4x -4x
3y = -4x + 9
Divide all terms by 3.
y = -4/3x + 3
The slope is -4/3.
Slope is in an equation that is perpendicular to this one.
The opposite of -4/3 is 4/3.
The reciprocal of that is 3/4.
Slope is 3/4.

Answer: 3/5

The slope formula for finding slope is "y sub two minus y sub one over x sub two minus x sub one." It does not matter which point you use for (x,y) one or (x,y) two. In this case, I'll use -1 as "x sub one" and 2 as "y sub one."
"Y sub two" is 5, and "x sub two" is four.
5 - 2 = 3
4 - (-1) = 4 + 1
4 + 1 = 5
Slope is 3/5.

Answer: y = -x + 6

As I've mentioned before, "b" is the y-intercept. The y-intercept is where the equation of the line crosses the y-axis and x is 0. Therefore, the point (0,6) is the y-intercept. For this problem, all you had to do was slip Slope in for "m" and the y-intercept in for "b" to arrive at your answer.

Answer: x - 2y = 4

Use the slope-intercept form of an equation to find your answer.
y = mx + b
y = -3, x = -2, m = 1/2, b is unknown.
-3 = 1/2(-2) + b
-3 = -1 + b
+1 +1
-2 = b
Final equation: y = 1/2x - 2
This is not an answer choice.
All answer choices are in standard form.
Let's change our equation to a standard form one.
y = 1/2x - 2
-1/2x -1/2x
-1/2x + y = -2
Make the coefficient in front of x a positive whole number.
-2(-1/2x + y = -2)
x - 2y = 4
Alas, we have our equation.
To check, plug the point in for x and y.
(-2) -2(-3) = 4
-2 + 6 = 4
4 = 4
The answer is most definitely x - 2y = 4.

Answer: undefined

This equation would be a vertical line on a graph. Slope is undefined because when you take two points on the line, say (3,1) and (3,3), and plug the numbers in the slope formula, you get 2/0. 2 cannot divide by 0 since nothing times 0 is ever going to give you 2, and therefore it is undefined. If the equation had been y = 3, Slope would have been 0. Plug (2,3) and (8,3) in the slope formula and you will get 0/6. 0 times 6 = 0 and in this case Slope is 0. Thanks so much for helping Slope out today! If you learned something from this quiz, don't hesitate to send me a message. So long for now!