Equations of Lines (Point Slope, Slope Intercept & Standard Form)

Equations of Lines

(Point Slope, Slope Intercept & Standard Form)

by Ms. G Collins

point slope form

How to write an equation of a line given 2 points

slope intercept form

There are two key facts we need to identify in the graph of a line.

1. slope

2. y-intercept

After we find these, we plug them into the equation.

Slope can be expressed in different ways:

Fill in the Blanks

In order to write the equation of a line through the points

(4,2) and (6,-6) you must first find the slope.

In order to write an equation in Slope Intercept Form, you need 2 things:

1. A slope (m)
2. A y-intercept (b)

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

It's easy when we are given the slope and the y-intercept....

But, what about when we have a piece missing?

Write an equation of the line in Slope Intercept Form that goes through the point (-3,7) and has a slope of 1/3

Fill in the Blanks

What is the value of b?

• Use the slope formula to find the slope 

• Once you have the slope, choose one of your 2 points (it doesn't matter which you choose - I kind of like to stick with the one on the left)

• Go through the exact same steps we just did in the previous slides

Now we just follow the exact same steps as the previous example.

* Substitute the values for x and y and m into the slope intercept formula (you will answer this on the next slide, so write it down!)

Fill in the Blanks

Using the equation $1=8\left(-3\right)+b_{\ }$   what is the y intercept?

Open Ended

Now we can write our Slope Intercept Equation :)

We have a slope of 8 and a y intercept of 25.

What is the equation of the line?

Multiple Choice

Write the equation in point-slope form of the line that passes through the given point and has the given slope.

(4, -7); m = -1/4

• y + 7 = -1/4(x - 4)

• y - 4 = -1/4(x + 7)

• y + 7 = 4(x - 4)

• y - 7 = -1/4(x - 4)

Multiple Choice

What is the slope intercept form for

y + 7 = -1/4(x - 4)

• y=-1/4x-6

• y=-1/4x+6

• y=7/4x+28

• y=1/4x+6

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= -3x + 35

• y + 5= -3(x + 10)

• y= -3x - 35

Multiple Choice

What is y intercept of the equation y - 3 = 4(x - 0)

• 4

• -3

• 3

• -4

To change from Standard Form to Slope Intercept Form, you solve the equation for y.

• First, add or subtract the "x" term.

• Second, divide by the coefficient (number in front of) y.

• Finally, simplify if you can.

Write 3x + 2y = 6 in slope intercept form

Multiple Choice

Which equation represents 4x - 2y = 6 in slope intercept form.

• y = 2x - 3

• y = -2x + 3

• $$y\ =\ \frac{1}{2}x\ -\ 3$$

• y = 2x + 8

Multiple Choice

Write x + 5y = 10 in slope intercept form.

• $$y=-5x\ +\ 2$$

• $$y\ =\ -\frac{1}{5}x\ +\ 5$$

• $$y\ =\ 5x\ +\ 2$$

• $$y\ =\ -\frac{1}{5}x\ +\ 2$$

Multiple Choice

Which represents  -2x - 3y = 12 in slope intercept form.

• $$y\ =\ -\frac{2}{3}x\ -\ 4$$

• $$y\ =\ \frac{2}{3}x\ -\ 4$$

• $$y\ =\ -\frac{2}{3}x\ +\ 4$$

• $$y\ =\ \frac{2}{3}x\ +\ 4$$