Gr 10 Math Ch 7: Gradient of a Line

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What does the gradient of a line represent?

The slope or steepness of the line (correct)

The distance between two points on the line

The midpoint between two points on the line

The position of the line on the graph

Which formula correctly represents the gradient between two points A(x₁, y₁) and B(x₂, y₂)?

m = (y₁ + y₂) / (x₁ + x₂)

m = (y₁ - y₂) / (x₂ - x₁)

m = (y₂ - y₁) / (x₁ - x₂)

m = (y₂ - y₁) / (x₂ - x₁) (correct)

What is the general form of the equation of a straight line?

y - y₁ = k (x - x₂)

y - y₁ = m (x - x₁)

y = mx + c (correct)

y = mx + k

For two lines to be parallel, what condition must their gradients satisfy?

Their gradients must be equal Signup and view all the answers

What is the product of the gradients of two lines that intersect perpendicularly?

-1 Signup and view all the answers

What gradient is associated with a horizontal line?

0 Signup and view all the answers

How can you express the equation of a straight line using point-slope form?

y - y₁ = m(x - x₁) Signup and view all the answers

What would be the slope of a line that is vertical?

Undefined Signup and view all the answers

If points A(2, 3) and B(5, 7) are connected by a straight line, what is the gradient of the line?

2.00 Signup and view all the answers

What is the y-intercept of the line given by the equation $y = 3x + 6$?

6 Signup and view all the answers

Given the equations of two lines, $y = 4x + 2$ and $y = -1/4x + 1$, do these lines intersect perpendicularly?

Yes, their gradients multiply to -1 Signup and view all the answers

Which of the following describes the gradient of a horizontal line?

Zero gradient Signup and view all the answers

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

3 Signup and view all the answers

How is the gradient of a line formed by points A(-1, -1) and B(4, 3) calculated?

By using the difference in y-values over the difference in x-values Signup and view all the answers

What can be concluded about two straight lines with gradients of 2 and -2?

They intersect at a 90-degree angle Signup and view all the answers

Which formula correctly represents the gradient of a line passing through points (2, 5) and (3, 8)?

$\frac{8 - 5}{3 - 2}$ Signup and view all the answers

What is the meaning of a constant gradient in the context of a straight line?

The line is straight and slopes at the same angle. Signup and view all the answers

If the gradient of a line is 3, what can be stated about a line perpendicular to it?

Its gradient will be -1/3. Signup and view all the answers

In the equation of a straight line, what does the term 'c' represent in the formula $y = mx + c$?

The y-intercept of the line. Signup and view all the answers

How is the gradient of a line determined from two points A(1, 2) and B(4, 6)?

Using the difference in y-coordinates divided by the difference in x-coordinates. Signup and view all the answers

Which statement is true regarding the gradients of parallel lines?

They have gradients that are equal. Signup and view all the answers

What can be concluded if a line has a gradient of zero?

The line is horizontal. Signup and view all the answers

Which of the following equations represents a straight line with a gradient of -2 and a y-intercept of 5?

$y = -2x + 5$ Signup and view all the answers

If the equation of a straight line is given as $y - 4 = -1/2(x - 6)$, what is the gradient?

-1/2 Signup and view all the answers

What does the term 'c' represent in the standard form of the straight line equation $y = mx + c$?

The y-intercept of the line Signup and view all the answers

If two lines intersect and their gradients are 3 and -1/3, what relationship do these lines have?

They are perpendicular. Signup and view all the answers

Which of the following statements is true if the gradient of a line is a negative value?

The line slopes downwards from left to right. Signup and view all the answers

Which expression correctly calculates the gradient of the line passing through the points A(3, 4) and B(7, 10)?

Gradient = $\frac{10 - 4}{7 - 3}$ Signup and view all the answers

For the equation of a straight line given as $y - 5 = 2(x - 3)$, what is the gradient?

2 Signup and view all the answers

If the equation of a line is derived to be $y = -4x + 7$, what can be stated about the slope as it relates to a line perpendicular to it?

The perpendicular line has a slope of -1/4. Signup and view all the answers

What is the main prerequisite for a set of lines to be classified as parallel?

They must have equal gradients. Signup and view all the answers

What can be concluded about two lines if one has a gradient of 0 and the other is undefined?

They are perpendicular. Signup and view all the answers

Given points A(-2, 5) and B(3, -1), what is the gradient of the line connecting these points?

−6/5 Signup and view all the answers

What is the equation of a straight line that has a gradient of 3 and passes through the point (1, 2)?

y - 2 = 3(x - 1) Signup and view all the answers

For lines WX and YZ to be parallel, what relationship should exist between their gradients?

m_{WX} = m_{YZ} Signup and view all the answers

If the gradients of two intersecting lines are 4 and k, what will be the value of k for the lines to be perpendicular?

−1/4 Signup and view all the answers

In which scenario will a line be considered horizontal?

When the gradient is zero Signup and view all the answers