Exploring Various Forms of Linear Equations

Forms of linear equations

By Hazim Budair

There are 3 main ways to write a linear equation

​Slope intercept, Standard form, and point slope form

​Slope intercept form

​

​Linear Equations

• A linear equation is​ an equation that forms a straight line when graphed on a coordinate plane.

• ​Slope intercept form is a type of linear equation in the form of Y=MX+B, where M is the slope an B is the y-intercept

​Y-intercept

​

• The y-intercept is the number in place of b in y=mx+b.

• This is the starting point when graphing a line!

• The y-intercept is where the line will cross through the y-axis on the coordinate plane.

• Pay attention to the symbol in front of b in the equation! This tells you if it is positive or negative (y=3x-4 means b= -4)

• ​The y-intercept written as an ordered pair is (0,b)... if b=-4, the ordered pair will be (0,-4)

​Slope

​

• The slope is a number that tells how steep the line will be.

• Slope is the m in y=mx+b. Slope is a fraction... if the number you have is not a fraction, put a 1 under it (3 = 3/1)

• After putting the y-intercept on the graph, the slope tells you where to go next. The top number is the rise (it tells you how far to go up if its positive, or down if its negative), and the bottom number is the run (it tells you how far to go to the right)

• ​If slope is positive, it will go up to the right ( / ), and if slope is negative, it will go down the the right ( \ )

Multiple Choice

What does "m" represent in y=mx+b?

• Slope

• Y-intercept

• X-intercept

• Nothing

Multiple Choice

What is the slope in the equation: y=9x+3

• 9x

• 9

• 3

Multiple Choice

What is the y-intercept in the following equation: y=-8x-10

• 1

• -8

• -10

Multiple Choice

 

What type of slope does the following graph have?

• i dont know

• positive

• negative

​Standard form

​Standard form

• Ax+By = C  

• ​We can use this to easily find the x-intercept and the y-intercept.

• ​The x-intercept is when y = 0. (x, 0)

• ​The y-intercept is when x = 0. (0, y)

• ​The x-intercept and y - intercept are written as coordinate points.

• ​The x-intercept is where it crosses the x-axis.

• ​​The y-intercept is where it crosses the y-axis.

​​Find the x-intercept for : -2x+5y\ =\ 10−2x+5y = 10  

​Step 1: Substitute 0 in for y: -2x+5\left(0\right)=10−2x+5(0)=10  

​Step 2: Simplify and solve for x

​Step 3: Write your answer as a coordinate point.

​

After you simplify: ​ -2x\ =\ 10−2x = 10  

​Divide both sides by -2: \frac{-2x}{-2}=\ \frac{10}{-2}−2−2x​= −210​  

​Simplify: x\ =\ -5x = −5  

​Write as a coordinate point: (-5, 0)​

​Find the y-intercept for : -2x+5y\ =\ 10−2x+5y = 10  

​Step 1: Substitute 0 in for x: -2\left(0\right)+5y=10−2(0)+5y=10  

​Step 2: Simplify and solve for y

​Step 3: Write your answer as a coordinate point.

​

After you simplify: ​ 5y\ =\ 105y = 10  

​Divide both sides by 5: \frac{5y}{5}=\ \frac{10}{5}55y​= 510​  

​Simplify: y=\ 2y= 2  

​Write as a coordinate point: (0, 2)

​To find the slope from a Standard Form Equation:

• ​Find the x-intercept and y-intercept. Then use a table or Desmos to find the slope between those two points.

Multiple Choice

What is the Standard Form of a linear equation

• Ax+By=C

• m = (y2-y1)/(x2-x1)

• y=mx+b

Multiple Choice

The ___________ is the point where a line crosses the x-axis.

• y-intercept

• domain

• range

• x-intercept

Multiple Choice

The y-intercept is the point where a line crosses the ___________.

• x-axis

• origin

• y-axis

• x-intercept

Multiple Choice

Which ordered pair could represent a y-intercept on a graph?

• (6, 0)

• (2, 0)

• (0, 4)

​Point Slope Form

point slope form​

How to write an equation of a line given 2 points

​What is point slope formula?

​The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The equation of a line is an equation that is satisfied by each and every point on the line. This means that a linear equation in two variables represents a line.

Remember to keep all the signs & simplify

​NOTE: when you have a negative

x1 or y1​

 

​4 Steps to Write an Equation

1. Insert the x₁, y₁ and m values into the formula.

​

2.​Change any double-negatives into positives.

​

3.Distribute.​

​

4. Move the number right by doing the opposite.​

Multiple Choice

Which of these represents point-slope form of a linear equation?

• y - y₁ = m(x - x₁)

• Ax + By = C

• y = mx + b

Multiple Choice

Write the equation of the line

in Point-Slope form that goes through

the point (10,5) and has a slope of -3

• y + 5= -3(x + 10)

• y - 5 = -3(x - 10)

• y= -3x - 35

Multiple Choice

The line with the equation

y + 1 = -3(x - 5),

contains the point (5, -1)

and has a slope of _______.

• 1

• -3

• y

Multiple Select

CONGRAJULATIONSSS!!!! YOU HAVE COMPLETED TODAYS LESSONS OM FORMS OF LINEAR EQUATIONS HOW DO YOU FEEL???!!!

• Need a little help

• dont understand anything

• getting there

• THIS IS THE EASIEST THING IN THE WORLD