More Easy Graph Formulas

More Easy Graph Formulas

TODAY’S LESSON: “Slope-Intercept Form” “Point-Slope Form” “Standard Form”

(2,3) (-2,0)

Every line has a formula that describes it! For every X, there is aY!

(5.45, 7.8)

(-1.5434,1.43423)

Even if a point isn’t exactly on a line, it still has an X & Y

Question: How many exact points are there on a line? I give hint: More than one… Answer:

• Remember when y is by itself:

y = 4x + 5 y-intercept = 5

SLOPE

• This “Y by itself” form is officially called “SLOPE-INTERCEPT FORM” ...because it tells you the SLOPE & the YIntercept of the line..

y = mx + b …where the m is the slope… …and the b is the y-intercept…

Guess what? You can find the Yintercept from ANY two points!

WITH ALGEBRA!!!

Example: Write the formula for a function that passes through (1,8) & (2,10).

STEP 1:We can find the slope with the two points!!

y = mx + b 8 – 10 -2 = = 1–2 -1

2

y=mx+b

Example: Write the formula for a function that passes through (1,8) & (2,10).

Step 2: Pick one of the points given, & plug them in for x & y ! Does it matter which one??

y = 2x + b 8 = 2(1) + b Nope! Both points are part of the formula! So either one works!

Example: Write the formula for a function that passes through (1,8) & (2,10).

STEP 3: Solve for “b” (to find the y-intercept)

8 = 2(1) + b 8=2+b -2

-2

6=b STEP 4: Write the formula !

2 x+ 6 b y=m

Write a formula that passes through the points (4,5) and (12,-5) 1) Find Slope 2) Find the Y-Intercept by plugging in the Slope and the X & Y of one of the points. 3) Re-write the formula with the Slope and Y-intercept plugged in.

Find the formula of a function that passes through these points: (9,-3) and (-3,-3) 1) Slope is…

2) Y Intercept is…

3) Formula!

In addition to the Slope-Intersect Form…

y = mx + b …there is another form called the PointSlope Form…

Point-Slope Form

For this type of formula, you only need to know any point, and the slope!

y – y = m(x – x ) 1

1

What this?? Trog no like little numbers!!

y – y1 = m(x – x1) Don’t freak out, Trog. The little numbers show you where to plug in the point you already know. It’s Easy

EXAMPLE: A point on a line is (4,6). The slope is ¾. Write the formula.

y – y1 = m(x – x1)

y – 6 = ¾(x – 4) Done!

REVIEW---

-Every function has a formula that can be written many different ways. -Slope-Intercept Form: A formula where the y is by itself…it tells us the y-intercept, and the slope. y = mx + b -Point-Slope Form: A formula where any point can be used along with the slope. y – y1 = m(x – x1)

Step-By-Step Question: Write out the Point-Slope & Slope Intercept formula for a function that passes through the points (9,17) & (-4, 5). Step 1: We need to find the slope! Step 2: Just plug it in and Point-Slope Form is now done!

17 – 5 = m= 9 – (-4)

12 13

y – y1 = m(x – x1)

y – 17 = 12 (x – 9) 13

Question: Write out the Point-Slope & Slope Intercept formula for a function that passes through the points (9,17) & (-4, 5).

STEP 3: Now we just y = mx + b need to find the 12 Y-Intercept to m = 13 x = -4 y = 5 complete the SLOPEINTERCEPT FORM. 5 = 12(-4) + b HINT: Use the Slope Intercept Form, and just plug one of the points!

13

Slope-Intercept Form:

y = mx + b Point-Slope Form:

y – y1 = m(x – x1)

One More Form… The third kind of form has both the X and Y on the same side of the equation:

x+y= This is called “STANDARD FORM”.