Equations of Straight Line Graphs - Part 2

This lesson follows on from ‘Using R to draw the equation of a straight line graph - Part 1’ and demonstrates how to use R to plot straight line graphs (y=mx+c) with different intercepts and negative gradients followed by questions on the observed differences.

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KS3: Plotting and finding the equations of straight line graphs (y=mx+c) - Part 2

Lesson objectives

Plotting and finding the equations of straight line graphs y=mx+c

Packages used in this lesson:

• tidyverse

Success criteria

• Plot a straight line graph y = mx+c
• Plot straight line graphs y = mx+c with different intercepts
• Plot a straight line graph y = mx+c with a negative gradient
• Find the equations of straight line graphs

Keywords

• slope
• gradient
• intercept
• x-axis
• y-axis

Worked Example 1

This is a worked example for you to follow.

We will show you how to plot the line graph for y=2x + 5.

x <- seq(from=-4, to=4, by=1) # sequence the x-axis from -4 to 4
y <- 2*x+5
mydata <- tibble (x,y)
ggplot(mydata) +
  aes(x,y) +
  geom_point () +
  geom_line (col='red')+
  geom_vline (xintercept = 0, col='black')+
  geom_hline (yintercept = 0, col='black')

Worked Example 2

We will now see what happens when you change the intercept c to a negative value.

1. y=3x+5
2. y=3x-5

Run the code in chunk2 by clicking on the little arrow on the right of the code chunk.

x <- seq(-4, 4) # sequence from -4 to 4
y1 <- 3*x+5
y2 <- 3*x-5
mydata <- tibble (x,y1,y2,y)
ggplot(mydata) +
  geom_line (aes(x=x, y=y1), col='red')+
  geom_line (aes(x=x, y=y2), col='blue')+
  geom_vline (xintercept = 0, col='black')+
  geom_hline (yintercept = 0, col='black')

Question: What is the same and what is different about these lines?

Answer:

Knit your document and check the output.

Activity 1

Draw these lines on a graph. Use the R code from chunk2 to help you. Remember to update the code with these new lines.

1. y=x+10
2. y=x-10

Question: What is the same and what is different about these lines?

Answer:

Activity 2

Now we will investigate m (the gradient). Draw these lines on a graph. Use R code from chunk2 to help you.

Run the code and knit the document.

1. y=-2x+5
2. y= 2x+5

Question: What is the same and what is different about these lines?

Answer:

Activity 3 Answer the following questions

Q1 In the equation y=mx+c, what happens when you change c?

Q2 What happens when you change m?

Write your answers here
Q1:

Q2:

Activity 4: Work out the equation from a line graph

Write down the equations of the following four lines on the graph below.

Knit the document to get a good view of the graph.

Write your answers here

Cyan line:

Red line:

Blue line:

Orange line:

KNIT YOUR DOCUMENT for the final time. This will be the version that your teacher will mark.

THE END

License and Citation: You can use, modify, and adapt any of the lessons, but please include the following attribution: RGirls Community. (2022, April 10). RGirls Lessons. Zenodo. https://doi.org/10.5281/zenodo.6436861