SLOPE-INTERCEPT FORM

Linear Equations

What is Slope-Intercept Form?

Slope-Intercept form is a way a line can be written.

It includes the slope and the y-intercept. The equation is y=mx + b,

where m = the slope and b = the y-intercept

An Example of Slope-Intercept

When given y=2/3x – 2, graph the linear equation.

First, what is the y-intercept? The y-intercept is -2! Then, find the slope…… The slope is 2/3. What does that mean? From each point, the line will rise up 2

and go right 3.

How do I Graph with Slope-Intercept?

The equation was y=2/3x – 2.

1st – Find the y-intercept…. -2, and place it on the graph

2nd – Find the slope….. The slope is 2/3. Rise/Run so the graph rises up 2 and runs 3.

3rd – Plot another point by following the slope. The next point will be at (3, 0).

4th – Connect the two with a line.

How Do I Write an Equation in Slope-Intercept Form When Given a Graph?

You need two things:SLOPE AND Y-INTERCEPT

1st – Find the y-intercept. Where does the line cross the y-axis? The y-intercept is 4!

2nd – Is it a positive or negative slope? Does it go up or down from left to right? It goes down so it’s NEGATIVE!

3rd – Find another point where the line crosses a grid intersection. There is one at (1, 1)!

4th – Count the rise/run from the y- intercept to the second point. The line went down 3 and right 1. So the slope is -3/1 which is -3.

So, if slope is -3 and the y-intercept is 4, what is the equation?......

y = -3x + 4

STANDARD FORM

Linear Equations

What is Standard Form?

Standard form is another way to write a linear equation.

The equation is …. ax + by = c A and B are coefficients for the variables. C is a number.

How Can I Graph from Standard Form?

You only need two points to draw a line. Standard Form gives you the two points…..the x and y intercepts!

3x - 6y = 12

1st – Find the x-intercept. Make y = 0 3x - 6(0) = 12 3x - 0 = 12 3x = 12 so…… x intercept is 4!!!

2nd – Find the y-intercept. Make x = 0 3(0) - 6y = 12 0 - 6y = 12 -6y = 12 so…… y = -2

Connect the dots by drawing a straight line. You have now graphed your line.

How Can I Write Slope-Intercept Equations in Standard Form?

When given y = 3x – 2, write the equation in standard form

Remember, Standard Form is ax + by = c.

Follow these easy steps: y = 3x – 2 -3x -3x (subtract 3x from each side)-3x + y = -2 or if you change the signs……3x – y = 2…..either answer is acceptable.

Let’s Try Some More

Write the following in Standard Form: y = 6x + 7 y = 3x – 4 y = -3x + 1 y = 4x Answers: y = 6x + 7 -6x + y = 7 or 6x – y = -7 y = 3x – 4 -3x + y = -4 or 3x – y = 4 y = -3x + 1 3x + y = 1 y = 4x -4x + y = 0 or 4x – y = 0

WHAT ABOUT FRACTIONS???

y = -¾ x + 4+ ¾x +¾x ( add ¾x to both sides)¾x + y = 4 (There’s an ugly fraction there…ugh!)How do you get rid of a FRACTION????Multiply by the denominator.... Multiply

EVERYTHING!!(4) (¾x) + (4)y = (4)4The four cancelled out the fraction….YEAH!!!3x + 4y = 16

Let’s Try Some More

y = ½x – 2 y = 1/3x + 4 y = ¼x – 2 y = 2/5x + 1 Answers: y = ½x – 2 -x + 2y = -4 or x – 2y = 4 y = 1/3x + 4 -x +3y = 12 or x – 3y = -12 y = -¼x – 2 x + 4y = -8 y = -2/5x + 1 2x + 5y = 5

How Do I Write Standard Form in Slope-Intercept Form?

SOLVE FOR Y!! When given 2x + 3y = 9, write in slope-intercept

form How do I solve for y??? First get y by itself…..subtract 2x from both sides 2x + 3y = 9 -2x -2x 3y = -2x + 9 (You have to write the x first) 3 3 3 (Then divide by 3…EVERYTHING) So y = -2/3x + 3

Let’s Try Some More

Write in Slope-Intercept Form1. 2x + 4y = 122. -3x + 5y = 103. x – 2y = -64. 6x – 4y = 3Answers:5. y = -½x +36. y = 3/5x + 2

7. y = ½x + 38. y = 3/2x – ¾

POINT-SLOPE FORM

Linear Equations

What is Point-Slope Form

It is another way to write a linear equation.

You need a point and the slope (hint: the name)

The formula is y – y1=m(x – x1)

m= the slope (x1, y1) is the point.

How do I write an equation in point slope form?

What is the equation for the line that runs through (3, 4) and has a slope of -½

m= -½ (3 is x1, 4 is y1) Put it into the equation!!! y- 4 = -½(x – 3) And that’s it…..Nothing More!!!What do you think will be the most

common mistake people will make?.....Putting the x and y’s in the wrong

places!!!

How can I graph from Point-Slope form?

Graph y – 1 = 1/3 (x – 2)

1st- What is the point?

(2, 1)

2nd – Place the point onto the graph

3rd- What is the slope?

m = 1/3

4th – From the point (2, 1) rise up 1 and go right 3.

5th – Finally, draw a line to connect the points.