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How do I write the equation of a straight line?

Slope intercept form equation examples

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Line V has a slope of -3/2 













  • Pick any two points to find the slope.
  • Let's use points A and B
  • Starting at point A counting three straight down for the rise
  •  Next count over two to the right to point B for the run.
  • Finally, is the slope positive or negative ?
  • As you move from left to right is the line sloping downward or upward?
  • This line is sloping downward therefore it has a negative slope.

Line V  intercepts the Y axis at point A therefore b equals 3



m = -3/2  ( slope)
b = 3  ( y intercept)

Now write it out in slope intercept form   y = -3/2x  + 3



Equation of a Straight Line-Slope Intercept Form

graph with slope =3/2
Line V
B


Slope Y Intercept Form
Hi Welcome to MooMooMath. Today we are going to look at the slope intercept form of a line. What form is that in? It is in y =mx + b In this formula m is the slope of the line and b is equal to the y intercept. What is a y intercept? The y intercept is where the y crosses the y axis. So the y axis is the long axis and in this example it crosses the y axis at positive 3 so I have a y intercept of positive 3 What is my slope? I pick two points on the line and I count. I go down three and over two. So I draw a right triangle and count three units down and two units across which is 3/2. I also notice that it is sloping down so it is a negative 3/2 Then all we do is plug an m and a b into the equation so I will plug negative 3/2 into my formula for the slope and 3 for b ( the y intercept) Let’s look at an overview. 
Slope Intercept Form
Y=mx =b
m = the slope of the line. You find the slope by counting the rise over the run
b = y intercept This is where the line crosses the y axis




The equation of a straight line in slope intercept form equals y=mx+ b

Directions for finding slope of a line

Plug the slope and y intercept into the slope intercept form equation y =mx + b

Write an equation for line V in slope intercept form.

A
The slope intercept form is one method of expressing a linear equation. A linear equation is an equation of a straight line. In the slope intercept form you use the slope and the y intercept to express the line.
graphing example slope intercept form
Write the linear equation of line a in slope intercept form.

Step 1. Use the points A and C Rise = 4,run = 2 slope = 4/2 = 2
Step 2. y intercept = 4
Step 3. Plug into slope intercept formula = y = 2x + 4

Write the linear equation of line a in slope intercept form.

Step 1. Use points A and C Rise = 2,run = -2 slope = 2/-2 = -1
Step 2. y intercept = -1
Step 3. Plug into slope intercept formula = y = -1x -1 

graph with points (-2,1) and (-1.0)

Slope intercept form from two points

You can also write the equation of a line in slope intercept form using two sets of points.

Step 1. Use the formula 
slope formula
When you have two points the x is always first and the y is always second.
Using the slope formula the y is always on top and the x is on the bottom.
2. Use the slope (m) and the x and y from one set of points and plug them into y=mx + b    (You can use either set of numbers )
3.Solve for b
4. Plug m and b into slope intercept form formula

Using the points (27,-18) (-20,3) Write the equation of the line in slope intercept form.
Find slope 


Plug the slope, and one order pair into the slope intercept formula
y=mx +b
3= -3(20) + b

Solve for b
3 = -60 + b
63 = b

Plug the slope and b into the formula.
 Y = -3x +63

-18-3/27-20=3

Slope intercept form in real life

Here are two video links of real world slope problems. The first real life problem involves using slope intercept in order to calculate which phone plan has the best annual cost.




Slope Real world problem 1


Real world problem using slope: The equation below represents the changing speeds of a car as it enters the expressway, travels on the expressway, and exits the expressway. Create a graph to represent the car’s different speeds.

Real world problem 2

girl on phone real life example slope intercept
real life example slope intercept (car driving)
C
C
Common Core Standard  8.F.A.3
Keywords: Straight line, linear function,slope
equation of a line y=mx+b
Value of y, the y axis runs up and down.
Slope.
Value of x, the x axis runs horizontally.
Where the line  crosses the y axis, also called the y intercept.
Notice with the slope of -3/2 you can count down three and over two. 
slope of a line on a graph
I think it is helpful if you see the slope intercept form on a graph. Remember the m represents the slope,B is the y intercept, y is the vertical distance, and the x represents the horizontal distance.
X
y
b