Gr 11 Math Ch 4: Equations of a Line

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What is the equation of a straight line in the two-point form?

y = mx + c
(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1) (correct)
y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)
y - y_1 = m(x - x_1)

Which form of the straight line equation is used when the gradient and one point on the line are known?

Two-point form
Gradient-point form (correct)
Gradient-intercept form
Slope-intercept form

What is the value of c in the equation y = mx + c?

slope of the straight line
gradient of the straight line
y-intercept of the straight line (correct)
x-intercept of the straight line

What is the equation of a straight line in the gradient-point form?

y - y_1 = m(x - x_1) (A) Signup and view all the answers

Which of the following is a summary of the key points of the straight line equation?

Two-point form: used when two points are known, Gradient-point form: used when the gradient and one point are known, Gradient-intercept form: used when the gradient and y-intercept are known (B) Signup and view all the answers

How do you derive the gradient-point form of the straight line equation?

By substituting m = (y_2 - y_1)/(x_2 - x_1) into the two-point form (C) Signup and view all the answers

What is the standard form of the straight line equation?

y = mx + c (A) Signup and view all the answers

Which of the following is not a form of the straight line equation?

Circle form (A) Signup and view all the answers

What is the main purpose of the two-point form of the straight line equation?

To find the equation of the line when two points are known (C) Signup and view all the answers

What is the value of y when x is 0 in the gradient-intercept form?

c (B) Signup and view all the answers

What is the definition of the constant c in the gradient-intercept form?

c = y_1 - mx_1 (D) Signup and view all the answers

How do you derive the gradient-intercept form from the gradient-point form?

By expanding the brackets and making y the subject of the formula (B) Signup and view all the answers

What is the gradient of the line when the equation is in the gradient-point form?

m = (y_2 - y_1) / (x_2 - x_1) (C) Signup and view all the answers

What is the formula for the gradient-point form of the straight line equation?

y - y_1 = m(x - x_1) (D) Signup and view all the answers

What is the main difference between the gradient-point form and the two-point form?

The gradient-point form uses the gradient and one point, while the two-point form uses two points (B) Signup and view all the answers

Which of the following is a common use of the two-point form?

Finding the equation of a line when two points are known (D) Signup and view all the answers

If two points on a line are (3, 4) and (6, 7), what is the value of x1 in the two-point form of the equation?

3 (D) Signup and view all the answers

What is the value of m in the gradient-point form when the gradient is 2 and the point is (3, 5)?

2 (D) Signup and view all the answers

If the equation of a line is y = 2x + 3, what is the y-intercept?

3 (D) Signup and view all the answers

What is the purpose of deriving the gradient-intercept form from the gradient-point form?

To find the y-intercept of a line (A) Signup and view all the answers

If the equation of a line is y - 2 = 3(x - 1), what is the value of the gradient?

3 (C) Signup and view all the answers

What is the relationship between the two-point form and the gradient-point form?

The two-point form is used when two points are known, and the gradient-point form is used when the gradient and a point are known (B) Signup and view all the answers

What is the advantage of using the gradient-intercept form?

It allows us to easily find the y-intercept (D) Signup and view all the answers

If the equation of a line is y = mx - 2, what is the value of the y-intercept?

-2 (B) Signup and view all the answers

What is the main advantage of using the gradient-intercept form over the two-point form?

It is easier to find the y-intercept of the line. (D) Signup and view all the answers

Which of the following is NOT a step in deriving the gradient-intercept form from the gradient-point form?

Subtracting x from both sides of the equation. (D) Signup and view all the answers

What is the primary purpose of the two-point form?

To find the equation of a line given two points. (B) Signup and view all the answers

Which form of the straight line equation is most useful when the gradient and y-intercept are known?

Gradient-intercept form. (A) Signup and view all the answers

What is the relationship between the gradient-point form and the two-point form?

They are equivalent forms. (D) Signup and view all the answers

Which of the following is an example of a real-world application of the gradient-intercept form?

All of the above. (D) Signup and view all the answers

What is the main difference between the gradient-intercept form and the two-point form?

The gradient-intercept form provides the y-intercept, while the two-point form does not. (C) Signup and view all the answers

Which of the following is a limitation of the two-point form?

It requires two points on the line. (A) Signup and view all the answers

What is the common requirement for using the two-point form and the gradient-point form of the straight line equation?

One point on the line is known. (C) Signup and view all the answers

What is the purpose of defining the constant c in the gradient-intercept form of the straight line equation?

To represent the y-intercept of the line. (D) Signup and view all the answers

When is the two-point form of the straight line equation more useful than the gradient-point form?

When two points on the line are known. (C) Signup and view all the answers

What is the advantage of using the gradient-intercept form of the straight line equation?