# Worksheet: Linear Functions in Different Forms

In this worksheet, we will practice writing linear functions in different forms, such as standard form and slope–intercept form.

Q1:

Write a linear function in the form , that has a slope of 3 and a -intercept of 8.

• A
• B
• C
• D
• E

Q2:

Calculate the slope and the -intercept for the function .

• A and
• B and
• C and
• D and
• E and

Q3:

Write the equation that represents the linear function shown in the given table.

 𝑥-value 𝑦-value −2 −1 0 3 4 5
• A
• B
• C
• D
• E

Q4:

What is the -intercept of the line passing through and ?

Q5:

True or false: The equation of a line intercepting the vertical axis at is .

• Afalse
• Btrue

Q6:

True or false: The equation of a line passing through the origin is .

• Atrue
• Bfalse

Q7:

Which of the following graphs represents the equation ?

• A • B • C • D • E Q8:

Which of the following graphs represents the equation ?

• A • B • C • D • E Q9:

What is the relation between the point and the line ?

• AIt lies on the line.
• BIt is the of the line.
• CIt is below the line.
• DIt is the of the line.
• EIt lies above the line.

Q10:

Find the slope and the -intercept of this straight line. • A,
• B,
• C,
• D,
• E,

Q11:

A straight line is defined by the equation .

Given that the point lies on the line, find an expression for in terms of , , and .

• A
• B
• C
• D
• E

Given also that the point lies on the line and is the slope of the line, find an expression for in terms of , , , and .

• A
• B
• C
• D
• E

By substituting in for and factorizing out , find the formula for the equation of the line.

• A
• B
• C
• D
• E

• A
• B
• C
• D
• E

Q12:

The general form for the equation of any linear function is . What do and represent?

• A represents the slope of the graph of the function, and represents the -intercept of the graph of the function.
• B represents the slope of the graph of the function, and represents the -intercept of the graph of the function.
• C represents the slope of the graph of the function, and represents the -intercept of the graph of the function.
• D represents the slope of the graph of the function, and represents the -intercept of the graph of the function.

Q13:

What is the -intercept of the function ?

Q14:

Which of the following equations represents the function drawn on the graph? • A
• B
• C
• D
• E

Q15:

Determine the equation of the straight line given in the diagram. • A
• B
• C
• D
• E

Q16:

Find the equation of the straight line that passes through the points and . Give your answer in standard form.

• A
• B
• C
• D
• E

Q17:

Given , , and , find the general equation of the straight line that passes through point and bisects .

• A
• B
• C
• D

Q18:

Find the Cartesian equation of the straight line passing through the point and parallel to the straight line whose equation is .

• A
• B
• C
• D

Q19:

Write the equation represented by the graph shown. Give your answer in the form . • A
• B
• C
• D
• E

Q20:

Write the equation represented by the graph shown. Give your answer in the form . • A
• B
• C
• D
• E

Q21:

A line has slope and passes through the point . What is the equation of this line?

• A
• B
• C
• D

Q22:

Write the linear equation in standard form.

• A
• B
• C
• D
• E

Q23:

Write the linear equation in standard form.

• A
• B
• C
• D
• E

Q24:

Write the linear equation in standard form.

• A
• B
• C
• D
• E

Q25:

Given that a linear function contains the points (2,3) and (0,6), find the slope of the function and state whether it is increasing or decreasing.

• A1.5, increasing
• B, decreasing
• C3, decreasing
• D2, decreasing