뒤로College Algebra Exam 3 Review: Graphing, Quadratics, & Rational Functions
스터디 가이드 - 스마트 노트
자료에 맞춘 맞춤형 노트, 핵심 정의, 예시, 맥락을 확장해 제공합니다.
Q1. Find the slope of the line that goes through the points (6, -3) and (6, -4).
Background
Topic: Slope of a Line
This question tests your understanding of how to calculate the slope between two points on a coordinate plane.
Key formula:
Where:
= slope
and are the coordinates of the two points
Step-by-Step Guidance
Identify the coordinates: and .
Plug the values into the slope formula: .
Calculate the numerator and denominator separately.
Try solving on your own before revealing the answer!
Final Answer: The slope is undefined.
Since the denominator is zero, the line is vertical and the slope is undefined.
Q2. Find the slope of the line that goes through the points (-3, 3) and (-2, 3).
Background
Topic: Slope of a Line
This question tests your ability to recognize horizontal lines and calculate their slope.
Key formula:
Step-by-Step Guidance
Identify the coordinates: and .
Plug the values into the slope formula: .
Calculate the numerator and denominator separately.
Try solving on your own before revealing the answer!
Final Answer: The slope is 0.
The numerator is zero, so the line is horizontal and the slope is zero.
Q3. Write the equation of the line passing through (-5, -7) and (-7, -2) in slope-intercept form.
Background
Topic: Linear Equations
This question tests your ability to find the equation of a line given two points.
Key formulas:
Slope:
Slope-intercept form:
Step-by-Step Guidance
Find the slope using the two points: .
Simplify the numerator and denominator.
Use one of the points and the slope to solve for in .
Write the equation in slope-intercept form.
Try solving on your own before revealing the answer!
Final Answer:
After calculating the slope and substituting one point, you get the equation in slope-intercept form.
Q4. Graph the equation in the rectangular coordinate system.
Background
Topic: Graphing Constant Functions
This question tests your ability to graph a horizontal line representing a constant function.
Key concept:
A constant function is a horizontal line at .
Step-by-Step Guidance
Recognize that means for all .
Draw a horizontal line at across the coordinate plane.
Try solving on your own before revealing the answer!
Final Answer: The graph is a horizontal line at .
This line extends infinitely left and right at .
