Linear Equations: Slope intercept and standard form

Linear Equations: Slope intercept and standard form

By Shalynne Orth

Linear Equations

• A linear equation in 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 and b is the y-intercept.

Multiple Choice

The graph of a linear equation is always a straight line.

• true

• false

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

Which of these represents slope-intercept form?

• y - y₁ = m(x-x₁)

• Ax + By = C

• y = mx + b

Multiple Choice

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

• y-intercept

• slope

• nothing

Multiple Choice

What is the slope in the equation: y=4x+3

• 3

• 4x

• 4

• x

Multiple Choice

What is the y-intercept in the following equation: y=-4x-5

• -4

• -4x

• 5

• -5

Multiple Choice

Which letter represents the y-intercept in y=mx+b?

• y

• m

• x

• b

Multiple Choice

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

• slope: 5

  y-intercept: (0,3)

• slope: 3/2

  y-intercept: (0,3)

• slope: 4

  y-intercept: (0,3/2)

• slope: 1/5

  y-intercept: (0,5)

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6

• y=3x-6

• y=3x+6

• y=6x+3

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3

• y=2/3-3

• y=2/3x-3

• y=2/3x+3

Graphing Slope-Intercept Form

How to graph y=mx+b

m=Slope

In y=mx+b, m is the slope. Slope is the rate of change of the line, or the change in y over the change in x. We say "Rise over Run" to remember this.

b=y-intercept

In y=mx+b, b is the y-intercept, which is where the line crosses the y-axis. If you have slope-intercept form, b is always your starting point when you are graphing a line.

Graphing in slope intercept form

• step 1: plot the y-intercept

• step 2: start at y-intercept and do rise over run with slope, then plot the point

Multiple Choice

When graphing a line in slope-intercept form, where will you start?

• On the x-axis at the x-intercept

• Start at the origin and use the slope to find the next point

• On the y-axis at the y-intercept

• Anywhere on the graph works

Multiple Choice

Which equation matches the graph?

(Hint: is the Y-INTERCEPT positive or negative, and is the SLOPE positive or negative?

• y= 0.5x - 5
• y= -0.5x - 5
• y= 0.5x + 5
• y= -0.5x + 5

Multiple Choice

Which equation matches the graph?

• y= 3x - 5
• y= -3x - 5
• y= 3x + 5
• y= 3x + 5

Multiple Choice

What is the equation of this line?

• y = 2x +2

• y = 2x -2

• y = -x + 2

• Cannot be Determined

Multiple Choice

Write the equation of the line.

• y= -1x-3

• y= -3x-1

• y=-1/3x-1

• y= -3x-3

Multiple Choice

Write the equation for the line in slope-intercept form.

• y= -1x+3

• y= 4x+3

• y=1/4x+3

• y= -4x+3

What if the line isn't given to me in slope-intercept form?

Sometimes, lines are in other forms, like standard form (for example, 6x+3y= 9). You can solve this for y to convert the equation to slope-intercept form, so you can easily graph using the slope and the y-intercept.

​

(Remember literal equations? This is an application of those!)​

Standard Form to Slope Intercept Form

Ax+By = C to y=mx+b

​

We will need to solve for y​ to get this in slope-intercept form so we can graph it.

​

1. Move the term with no y over to the other side

2. Divide both sides by B​

​

Multiple Choice

When solving 3x + 2y = 12 for y, to put it into slope intercept form, what will you do first?

• Add 3 to both sides

• Subtract 3 from both sides

• Add 3x to both sides

• Subtract 3x from both sides

Multiple Choice

When solving 2x + 5y = 15 for y, to put it into slope intercept form, what is the 1st step?

• Add 2 to both sides

• Subtract 2 from both sides

• Add 2x to both sides

• Subtract 2x from both sides

Multiple Choice

Solve for y (slope intercept form): 

                      2x + 3y = 12

• y= 6x + 2

• $$y\ =\ -\frac{2}{3}x\ +4$$

• $$y\ =\ -\frac{3}{2}x\ +\ 4$$

• y = 2x + 6

Multiple Choice

Lets try another one:

Solve for y:

   15x + 5y = 25

• $$y\ =\ 15x\ -\ 5$$

• $$y\ =\ -5x\ +\ 15$$

• $$y\ =\ -3x\ +5$$

Multiple Choice

Solve 5x+3y=8 for y.

• $$y=\frac{5}{3}x+\frac{8}{3}$$

• undefined

• $$y=-5x+8$$

• $$y=x$$

​Standard Form

​Another way to graph standard form is to find the x- and y-intercepts.

​

x-intercept is when y=0, and y-intercept is when x=0.​

Graph

• Graph your x-intercept

• Graph your y-intercept

• Draw a line connecting the 2 points

Multiple Choice

^{What is the x- intercept of the line?}

• (0, 1)

• (1, 0)

• (-1, 0)

• (0, -1)

Multiple Choice

What are the x- and y- intercepts, respectively, on this graph?

• (0,5), (0,5)
• (5,0), (5,0)
• (5,0), (0,5)
• (0,0), (5,0)

Multiple Choice

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

• (6, 0)
• (0, 4)
• (-1, 3)
• (2, 0)

Multiple Choice

Give the y-interecept
3x + y = 5

• (-3, 0)
• (0,5)
• (5, 0)
• (0, -3)

Multiple Choice

Give the x-intercept
3x + 8y = 24

• (8, 0)
• (0, 8)
• (3, 0)
• (0, 3)

Multiple Choice

What is the y -intercept?

• 12

• 8

• -3

• 1

Multiple Choice

Given the list of ordered pairs, what is the x-intercept?

(8,10), (3, -4), (0, 8), (4, -3), (9, 0)

• (8,10)

• (9,0)

• (0,8)

• All of the above.