# Worksheet: Equation of a Straight Line: General Form

In this worksheet, we will practice finding and writing the equation of a straight line in general form.

Q1:

Write the equation of the line that passes through the points and in the form .

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• B
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• E

Q2:

A line passes through the points and .

Find the gradient of the line.

Find the coordinates of the point at which the line intercepts the -axis.

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Hence, write the equation of the line in the form .

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Q3:

Write the equation of the line with slope and -intercept in the form .

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Q4:

What are the - and - intercepts of the line ?

• A2, 12
• B3, 12
• C2, 3
• D3, 2

Q5:

A line passes through and cuts out a triangle of area 32 with the two coordinate axes. What is its equation?

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Q6:

Find all the lines that pass through and whose - and -intercepts combined distances from the origin is 12.

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• D

Q7:

Given that the coordinates of the points and are and , respectively, and the point divides internally in the ratio , determine the equation of the straight line passing through the points and .

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• D

Q8:

Determine the area of the triangle bounded by the , the , and the straight line .

• A112 area units
• B14 area units
• C56 area units
• D28 area units

Q9:

Determine the equation of the straight line having a direction vector of , given that the line intersects the positive part of the at a point that is 6 units away from the origin.

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Q10:

A line passes through the points and . Work out the equation of the line, giving your answer in the form .

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Q11:

Let be the point and be the point . Which of the following points is on ?

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Q12:

Determine the equation of the line which cuts the -axis at 4 and the -axis at 7.

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Q13:

Find the equation of the line that passes through the points and , giving your answer in the form .

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Q14:

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

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Q15:

A straight line has the equation . What is the slope of the line?

Q16:

If the slope of the straight line equals , find the value of .

Q17:

Find the slope of the line and the -intercept of this line.

• A,
• B, 1
• C,
• D,

Q18:

Which of the following is a Cartesian equation for a straight line that passes through the point with direction vector ?

• A
• B
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• D