9th Grade Math Unit 3

What is a linear relationship?

A relationship between 2 variables that forms a line when graphed. Has a independent and dependent variable. This type of relationship also should have a constant rate of change.

What are nonlinear functions?

Functions that when are graphed do not form a straight line. Also functions that do not have a constant rate of change.

What is the slope of a line?

The rate of change in a function. Greater rate of change leads to a steeper line when graphed.

What is the slope formula to find slope?

y₂ - y₁ / x₂ - x₁

What does a slope of zero mean?

That the y value is not changing.

What does a undefined slope mean?

That the x value is not changing.

What is the slope intercept form?

y=mx+b

What is m and b in the point slope form?

in y=mx+b, m is the slope, and b is the y intercept.

What is the point slope form?

y - y₁=m(x-x₁₎

What is a benefit of using the point slope form?

You can write a linear equation in point slope form without the y intercept, and you can find the y intercept by solving the equation.

What is the standard form of a line?

Ax + By = C

What are a few requirements of the standard form?

Ax + By = C. A, or B, or C can only be integers. A cannot be any number less then 0, A and B cannot be 0 at the same time, and A and B must be on the same side of the equation. A, B, and C, must all have a greatest common factor of 1.

How do you find the slope with the standard form? Ax + By = C

-A/B (b is positive)

How do you find x and y intercepts in the standard form? Ax + By = C

By setting y or x to 0.

How do you graph a standard form equation? Ax + By = C

By finding both intercepts and drawing a line to connect them.

What does it mean when Y is 0 in standard form? Ax + By = C

x is constant and a vertical line is formed, or a undefined slope.

What does it mean when x is 0 in standard form? Ax + By = C

When X is 0, Y is constant and a horizontal line is formed (slope of 0)

How do you turn a graph into standard form?

First start by writing the graph in point slope formula, and after solving the equation, subtract x on both sides to bring x and y on the same time. Then multiply the equation so that x is not negative and is a positive integer or 0. A proper equation in standard form should look like this, 4x -5y = 9.

How do you write a linear equation in point slope form with only 2 points on the graph?

First by finding the slope with the slope formula, and then using those 2 points in point slope form to find the y intercept after solving.

What is direct variation?

something that is written like this y=kx. (k is the constant of variation

How is k found in direct variation?

with the formula k=y/x in any point besides 0,0.

What must the value of b be in direct variations?

0, this is so that the graph starts from the origin. (0,0)

What is the explicit formula?

f(n) = m(n) + b. A recursive formula used to find the next value without the previous two term values.

What is m and b in the explicit formula?

in f(n) = m(n) + b. M represents the common difference. N represents the sequence term number, and b represents the starting value (first number of the sequence)