# Equations and Graphs of Straight Lines Task

**Question description**

**Question 1: The Gradient**

a) Plot the following lines on the same set of axes.

b) State the gradient of each line.

What part of the equation is related to the line’s gradient?

c) (i) Which line has the steepest gradient?

(ii) Which line has the least steep gradient?

(iii) How does the gradient affect the steepness of a line?

**Question 2: The y intercept.**

a) Plot the following lines on the same set of axes given below:

b) Read off the y intercept for each line. Fill in the table.

What part of the equation is related to the line’s y intercept?

**Question 3**

The graph shows y=2x-1 and y=2x+6

a) In the table give the gradient and y intercept for each line.

b) Draw in y=2x+3 on the graph.

c) What can you say about the lines that have the same gradient?

d) The graph shows y=-2x+4

Draw y=2x+4 on the graph.

Gradient=?

Y intercept=?

**Question 4**

The cost of making batches of plastic parts is given by the equation:

Cost (in $’000)=2×number of batches+10

C=2n+10

a) Up to 50 batches are made. Draw a graph of cost by plotting a few points.

b) Work out the cost of making 21 batches.

c) What cost has to be covered even if no batches are made?

**Question 5**

Fill in the tables, plot the points and connect them to graph the line.

a)

b)

**Question 6**

Graph the following equations by finding the x and y intercepts

a) y=4x-6

b) y=-3x+2

**Question 7**

Find the equations of the following straight lines:

a) Gradient-3,passing through(4,5)

b) Passing through(-1,-8)and(2,10)

c) Gradient 5,passing through(1,-4)

d) Passing through(-6,4) and (2,0)

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