Starter Which pair of lines are parallel? Which pair of lines are perpendicular? How do you know? PRINT

Which graph is parallel to y = 3x + 6   y = -3x - 6 y = 3x - 2   How do you know?

Which graph is perpendicular to y = 3x + 6   y = -3x - 6 y = 3x - 2   How do you know?

Which graph has the same y-intercept as y = 3x + 6   y = -3x - 6 y = 3x - 2   How do you know?

Which graph has the same x-intercept as y = 3x + 6   y = -3x - 6 y = 3x - 2   How do you know? Discuss: What is the x-intercept?

What is the y-intercept? Here is the graph y = 3x + 6: What is the y-intercept?

Where is the y-intercept found on the graph? Here is the graph y = 3x + 6: Where is the y-intercept found on the graph?

Where is the x-intercept found? Here is the graph y = 3x + 6: Where is the x-intercept found?

What is the x-intercept? Here is the graph y = 3x + 6: What is the x-intercept?

Here is the graph y = 3x + 6: When we are given a graph it is easy to read off the coordinate for the x-intercept What can you say is always true about the x-intercept of any line? We know that the y coordinate at this point is 0: ( ? , 0 ) Discuss: How we could work out the x coordinate at this point if we don’t have a graph?

Where would y = 3x + 6 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 0 = 3x + 6 Let’s check on Desmos -6 -6 -6 = 3x ÷3 ÷3 -2 = x The line y = 3x + 6 crosses the x-axis at -2 Its x-intercept is -2

Where would y = 2x - 8 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 0 = 2x - 8 +8 +8 8 = 2x ÷2 ÷2 4 = x The line y = 2x - 8 crosses the x-axis at 4 Its x-intercept is 4

On your whiteboards … Where does y = 2x – 6 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 0 = 2x - 6 +6 +6 6 = 2x ÷2 ÷2 3 = x The line y = 2x - 6 crosses the x-axis at 3 Its x-intercept is 3

On your whiteboards … Where would y = 6x + 3 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 0 = 6x + 3 -3 -3 -3 = 6x ÷6 ÷6 -0.5 = x The line y = 6x + 3 crosses the x-axis at -0.5 Its x-intercept is -0.5

On your whiteboards … Where would y = -2x + 8 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 0 = -2x + 8 -8 -8 -8 = -2x ÷-2 ÷-2 4 = x The line y = -2x + 8 crosses the x-axis at 4 Its x-intercept is 4

On your whiteboards … Where would y = -3x - 12 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 0 = -3x - 12 +12 +12 12 = -3x ÷-3 ÷-3 -4 = x The line y = -3x - 12 crosses the x-axis at -4 Its x-intercept is -4

We know that when a line crosses the x-axis,   We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line.   +3 +3   ÷1/2 ÷1/2 6 = x   Its x-intercept is 6

We know that when a line crosses the x-axis,   We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line.   -2 -2   ÷1/4 ÷1/4 -8 = x   Its x-intercept is -8

On your whiteboards … Where would 2y = 3x + 2 cross the x-axis? We know that when a line crosses the x-axis, the y coordinate is 0, so substitute y = 0 into the equation of the line. 2(0) = 3x + 2 -2 -2 -2 = 3x ÷3 ÷3      

Find the x-intercept of the following lines and make a sketch of each: 1) y = 4x – 12 2) y = 6x + 4 3) y = -2x – 3 4) y = -3 - 3x 5) y = ½x - 6 Challenge: 4y = 2x + 2

You will receive a set of cards and a grid. You will be asked about various attributes of the straight lines. For example: which lines are parallel, which have the same y-intercept etc… If you know you are going to have to compare the lines, what might be a good first step to prepare? You may want to set students off at this point or take them through the first steps. Find the gradient and y-intercept for each card as your first step.

Complete the activity in your pairs. Put a pair of linear equations in each box of the table. Make sure you justify each answer as you work and that both of you agree with what is being said. Create your own rule connecting the pair of lines that are left over. When you are happy with your answers, stick the equations into the table.

What was the question? Find as many as you can. In pairs: The answer is y = 2x + 5 What was the question? Find as many as you can.