unit 4 linear functions test study guide - wordpress.com
TRANSCRIPT
![Page 1: Unit 4 Linear Functions Test Study Guide - WordPress.com](https://reader033.vdocuments.net/reader033/viewer/2022050218/626ea38509b5d40d7c6c3f32/html5/thumbnails/1.jpg)
IB Math Studies Yr 1 Final Exam Review
Name_________________________________ Date: ____________
For this quiz, you need to be able to:
1. Find the gradient, distance, and midpoint of 2 points on a line.
2. Identify the gradient and y-intercept of a line from a graph or equation.
3. Write the equation of a line in gradient-intercept form (๐ฆ = ๐๐ฅ + ๐)
4. Write the equation of a line in standard form (๐๐ฅ + ๐๐ฆ + ๐ = 0)
5. With gradient, you need to be able to find parallel and perpendicular gradients.
PART 1: Find the gradient, distance, and midpoint of 2 points on a line.
Distance formula
The distance formula is used to find the length between any 2 points.
The distance (or length) of a line is calculated by using the formula below from the โPrior learningโ
section (page 2) of the IB Formula Booklet.
Example: Find the length between (4, -5) and (-1, -1).
Unit 4 Linear Functions Test Study Guide
![Page 2: Unit 4 Linear Functions Test Study Guide - WordPress.com](https://reader033.vdocuments.net/reader033/viewer/2022050218/626ea38509b5d40d7c6c3f32/html5/thumbnails/2.jpg)
IB Math Studies Yr 1 Final Exam Review
Midpoint formula
The midpoint formula is used to find the โmiddle pointโ between any 2 points.
The midpoint of any 2 points can be found by using the formula below from the โPrior learningโ section
(page 2) of the IB Formula Booklet.
Example: Find the midpoint between (-9, -1) and (-3, 7).
Gradient formula (slope)
The gradient formula (slope) is used to calculate the direction and steepness between 2 points on a line.
The gradient of any 2 points can be found by using the formula below from the โTopic 5 โ Geometry
and trigonometryโ section (page 5) of the IB Formula Booklet.
Example: Find the gradient between (-1, 3) and (5, 1).
![Page 3: Unit 4 Linear Functions Test Study Guide - WordPress.com](https://reader033.vdocuments.net/reader033/viewer/2022050218/626ea38509b5d40d7c6c3f32/html5/thumbnails/3.jpg)
IB Math Studies Yr 1 Final Exam Review
PART 2: Identify the gradient and y-intercept of a line from a graph or equation.
Equation
Find the gradient and y-intercept of 4x + 3y = 9.
Graph
Find the gradient and y-intercept of the graph
below.
๐ =๐๐๐ ๐
๐๐ข๐=
1
2 ๐ = 1
PART 3: Write the equation of a line in gradient-intercept form (๐ฆ = ๐๐ฅ + ๐)
The equation of a line in slope-intercept form tells us two key pieces of information.
Here are two examples of how to write the equation of a line given the gradient and a point.
![Page 4: Unit 4 Linear Functions Test Study Guide - WordPress.com](https://reader033.vdocuments.net/reader033/viewer/2022050218/626ea38509b5d40d7c6c3f32/html5/thumbnails/4.jpg)
IB Math Studies Yr 1 Final Exam Review
Here is an example of how to write the equation of a line given 2 points.
![Page 5: Unit 4 Linear Functions Test Study Guide - WordPress.com](https://reader033.vdocuments.net/reader033/viewer/2022050218/626ea38509b5d40d7c6c3f32/html5/thumbnails/5.jpg)
IB Math Studies Yr 1 Final Exam Review
PART 4: Write the equation of a line in standard form (๐๐ฅ + ๐๐ฆ + ๐ = 0)
When you are asked to write an equation in standard form, it is asked as:
โPlease write the following equation in the form ๐๐ + ๐๐ + ๐ = ๐ , where a > 0, and ๐, ๐, ๐๐๐ ๐ โ โค.โ
When you see these directions:
1. Write the equation in gradient-intercept form.
2. Get everything to one side of the equation (Set equation = 0)
3. Make sure that a or the coefficient with a is positive
4. Multiply by the denominator of the fraction in order to make a, b, and c integers.
Here is an example of how to write the equation of a line in standard form when given 2 points.
A line passes through the points (-2, 6) and (1, 4). Write down the equation of in the form ๐๐ฅ + ๐๐ฆ + ๐ = 0, where ๐, ๐, and ๐ are integers and ๐ > 0.
First write the equation in gradient-intercept form (๐ฆ = ๐๐ฅ + ๐)
๐ =๐ฆ2 โ ๐ฆ1
๐ฅ2 โ ๐ฅ1=
4 โ 6
1 โ (โ2)=
โ2
3= โ
2
3
๐ฆ = ๐๐ฅ + ๐
๐ฆ = โ2
3๐ฅ + ๐
Use one of the given points to find โcโ. Letโs use (1, 4)
4 = โ2
3(1) + ๐
4 = โ2
3+ ๐
๐ =14
3
๐ฆ = โ2
3๐ฅ +
14
3
Now convert to standard form (๐๐ฅ + ๐๐ฆ + ๐ = 0)
๐ฆ = โ2
3๐ฅ +
14
3
0 = โ2
3๐ฅ โ ๐ฆ +
14
3 (divide all by -1)
0 =2
3๐ฅ + ๐ฆ โ
14
3 (multiple all by 3)
0 = 2๐ฅ + 3๐ฆ โ 14
![Page 6: Unit 4 Linear Functions Test Study Guide - WordPress.com](https://reader033.vdocuments.net/reader033/viewer/2022050218/626ea38509b5d40d7c6c3f32/html5/thumbnails/6.jpg)
IB Math Studies Yr 1 Final Exam Review
PART 5: With gradient, you need to be able to find parallel and perpendicular gradient.
Two lines are parallel if and only if they have the same gradient.
Same gradient means equal slopes
Two lines are perpendicular if and only if their equations form a 900 angle at their point of intersection.
We can also determine whether two lines are perpendicular if their gradients
are negative reciprocals of each other
Negative reciprocal means to flip and negate a fraction.