Writing the Equation of a Line Given Two Points

Writing the Equation of a Line Given Two Points

by Phillip Brown

​Remember

​Learning does NOT work like is shown in the picture. It requires time and repetition. Taking good notes uses both time and repetition.

To learn ... take good notes

​Write down anything that is new, has a title, any and all definitions, any concept, all goals, and of course ...

​

​Title your notes, write questions you have, and do all examples.

​

​Leave space!

​By the end of today you should be able to honestly say,

​I can write the equation of a line in slope - intercept form (y = mx + b) if I am given two points.

Poll

I wrote down the thing I should be able to do by the end of the lesson.

• Yes

• No

• No, but I clicked yes.

• No, but I am going to fix that right now!

​You need to be good at two old skills today.

​Slope formula

​

​writing an equation given a point and a slope.

Multiple Choice

What is the slope of the line with points (2, 1) and (3, -5)?

(Write your work in your notes before answering.)

• 6

• -6

• $$\frac{1}{6}$$  

• $$-\frac{1}{6}$$  

​What is the equation of the line that has a slope of 2 and passes through (2, -4)?

​Step 1: Start with substituting the provided information into y = mx + b.

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​Step 2: Simplify (multiply or reduce m times x)

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​Step 3: Solve for b.

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​Step 4: Write your equation.

​What is the equation of the line that has a slope of 2 and passes through (2, -4)?

Step 1: y = mx + b --> -4 = 2(2) + b

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​Step 2: -4 = 4 + b

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​Step 3: -8 = b

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​Step 4: y = 2x - 8

Fill in the Blanks

What is the equation of the line that has a slope of  $-\frac{1}{3},$   and passes through the point (-6, 5)?

​Write the equation of the line that contains the points (4, 2) and (6, 3).

​Step 1: Use the slope formula to find the slope.

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​Step 2: Pick one of the points to use as x and y.

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​Step 3: Plug in your slope and one of the points.

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​Step 4: Solve for b.

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​Step 5: Write your equation.

Multiple Choice

What is the slope of the line with the points (4, 2) and (6, 3)?

• 2

• -2

• $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

​Step 2: Pick a point ...

​It won't matter which point you pick, you get the same answer either way.

Multiple Select

What is the equation of the line with a slope of  $$\frac{1}{2},$$  and that passes through the point (4, 2)?

Write the work out in your notes, do NOT guess.  Get help if you need, use your notes.

• $$y=\frac{1}{2}x+0$$  

• $$y=\frac{1}{2}x\$$  

• $$y=\frac{1}{2}x-4$$  

• Answer not shown.

Multiple Select

What is the equation of the line with the slope of  $$\frac{1}{2},$$  that passes through the point (6, 3)?

Write the work out in your notes, do NOT guess.  Get help if you need, use your notes.

• $$y=\frac{1}{2}x+0$$  

• $$y=\frac{1}{2}x\$$  

• $$y=\frac{1}{2}x-4$$  

• Answer not shown.

​Slope 1/2, point (6, 3).

Multiple Choice

What is the equation of the line with the points (0, 3) and (5, -1)?

• $$y\ =\ -\frac{4}{5}x\ -3$$  

• $$y=-\frac{4}{5}x\ +\frac{12}{5}$$  

• $$y=-\frac{5}{4}x+3$$  

• Answer not shown.

​What are the two points shown on the graph?

​Does your answer to the previous multiple choice question answer the graph?

Poll

I feel confident finding the slope by using the formula.

• Very

• Yes

• Negatives mess me up.

• I need to help myself.

Poll

I can find the equation of a line if I am given a point and a slope.

• No problem, brochacho.

• Yeah, I can handle that, protatochip.

• Well, fractions cause me trouble.

• Bruh, what is slope?

​To find the equation of a line if you're given two points, you need to be good at ...

​1. Slope formula

​2. Finding the equation of a line given a slope and a point.

​

​If you're struggling with one of these, you need some practice.

Poll

I can find the equation of a line given two points.

• Yup, got it.

• I need a little practice, but know the steps.

• I get a little confused, but think I got it.

• I'm in big trouble ... but am responsible for myself and will fix it!