IB Math Studies Yr 1

Name_________________________________ Date_______________

4-6 Determining Intercepts Today’s Learning Goals:

How do I find the x and y intercepts of a linear function algebraically?

How do I find the x and y intercepts given a graph?

Warm Up: Answer the following questions in order to prepare for today’s lesson.

1. Determine the coordinates of the y-intercept

of the line graphed below.

2. Determine the coordinates of the x-intercept of the

line graphed below.

What similarities are there between these two questions?

What similarities are there between your two solutions?

What is one major difference in your two solutions?

IB Math Studies Yr 1

What is an intercept?

An intercept is the _________at which the graph of a function crosses either the ____ or _____ axis.

x-intercept: The coordinates where the function crosses the x-axis.

y-intercept: The coordinates where the function crosses the y-axis.

**Note** Make sure to write your answer as a coordinate (ordered pair)

Find the coordinates of the y – intercepts of the graph below:

What do each of these solutions have in common?

Note: Don’t confuse this with intersect!

That is something different

IB Math Studies Yr 1

Steps for finding the y – intercept algebraically:

1. Plug in zero for the x coordinate

2. Solve the equation for y

3. State the y-intercept as a coordinate if it asks to do so

Example:

Find the coordinates of the y – intercept of the equation: 2𝑦 − 3𝑥 = 11, algebraically

Find the coordinates of the y – intercepts of the equations below algebraically:

1. 𝑦 =7

4𝑥 + 6

2. −5

2𝑥 + 𝑦 = 12

3. 4𝑦 = 8𝑥 + 4

4. 𝑦 = −𝑥

IB Math Studies Yr 1

Find the coordinates of the x – intercepts of the graph below:

What do each of these solutions have in common?

IB Math Studies Yr 1

Steps for finding the x – intercept algebraically:

4. Plug in zero for the y coordinate

5. Solve the equation for x

6. State the x-intercept as a coordinate if it asks to do so

Example:

Find the coordinates of the x – intercept of the equation: 2𝑦 − 3𝑥 = 11.

Find the coordinates of the x – intercepts of the equations below algebraically:

5. 𝑦 =7

4𝑥 + 6

6. −5

2𝑥 + 𝑦 = 12

7. 4𝑦 = 8𝑥 + 4

8. 𝑦 = −𝑥

IB Math Studies Yr 1

IB Style Questions

Error Analysis:

1. State the coordinates of the x-intercept of the following equation: 𝑥 − 2 = 3𝑦 +7

Student work:

Your work:

State the two errors that were made:

1.

2.

IB Math Studies Yr 1

Practice: 1. State the coordinates of the x and y intercepts of the following linear equations.

1.

2.

3.

4.

5.

6.

7.

2. State the coordinates of the x and y intercepts of the following linear equations.

𝑦 − 4 = 3

2𝑥 – 1

𝑦 + 2 = 5𝑥 − 4

4x + 2y = 6

3 − 3𝑦 = 6(𝑥 + 4)

IB Math Studies Yr 1

Name:____________________________

Date:___________________

4-6 Exit Ticket

1. Determine the equation of the line that passes through the following points: A(4, 7) and B(8, 10) in

gradient intercept form.

2. Write the above equation in the form: 𝑎𝑥 + 𝑏𝑦 + 𝑑 = 0 , where a > 0, and 𝑎, 𝑏, 𝑎𝑛𝑑 𝑑 ∈ ℤ

\

3. Find the coordinates of both the x and y intercept algebraically.

IB Math Studies Yr 1

Name_________________________________ Date_______________

4-6 Homework

1. Determine the gradient and y-intercept of: 9𝑦 = 𝑥 – 18. Clearly mark each answer!

2. Does (4, -3) lie on the line: 3𝑦 − 6𝑥 = 18? Justify with mathematics.

3. State the x and y intercepts of: −8 = 2𝑦 − 1𝑥

1. State the coordinates of both the x and y intercepts of the graph below.

a. What is the equation of the line?

IB Math Studies Yr 1 4. The four diagrams below show the graphs of four different straight lines, all drawn to the same scale. Each

diagram is numbered and c is a positive constant.

In the table below, write the number of the diagram whose straight line corresponds to the equation in the

table.

Equation Diagram number

y = c

y = – x + c

y = 3 x + c

y = x + c

5. Graph the line: x = 5 on the following graph.

x

x

x

x

y

y

y

y

c

c

c

c

Number 1

Number 2

Number 3

Number 4

0

0

0

0

3

1