Gr 10 Math Ch 5: Linear Functions

What is the first step required to calculate the y-intercept of the equation in the form of $y = mx + c$?

Calculate the change in $y$ and $x$.

Let $x = 0$ to find the point $(0, c)$. (correct)

Let $y = 0$ to find the x-intercept.

Determine the slope $m$ of the line.

If the slope $m$ of a line is negative, what does this indicate about the graph?

The line rises to the right.

The line is horizontal.

The line falls to the right. (correct)

The line is vertical.

How is the steepness of a line represented mathematically?

By the ratio of the x-intercept to the y-intercept.

By the variable $c$.

By the y-intercept value alone.

By the ratio of vertical change to horizontal change, $m = rac{ ext{change in } y}{ ext{change in } x}$. (correct)

Which statement correctly describes the dual intercept method for sketching graphs of the form $y = mx + c$?

It involves calculating only the x-intercept and y-intercept. Signup and view all the answers

What points are used to define a straight-line graph in the gradient and y-intercept method?

The y-intercept and the gradient $m$. Signup and view all the answers

What does the value of the constant $m$ affect in the equation $y = mx + c$?

The slope of the graph Signup and view all the answers

If the value of $m$ is negative, how does the graph behave?

It slopes downwards from left to right Signup and view all the answers

Which statement about the y-intercept $c$ is correct?

$c$ affects where the graph cuts the x-axis Signup and view all the answers

What is the domain of the function $f(x) = mx + c$?

All real numbers Signup and view all the answers

What happens to the graph of $y = mx + c$ when $c$ is greater than zero?

The graph shifts vertically upwards Signup and view all the answers

How can the y-intercept of the graph be calculated?

By setting $x = 0$ in the equation Signup and view all the answers

When $m = 0$ in the equation $y = mx + c$, what is the nature of the graph?

The graph is a horizontal line Signup and view all the answers

What is the range of the function $f(x) = mx + c$?

All real values of $f(x)$ Signup and view all the answers

What is required to calculate the second point for plotting a graph using the gradient and y-intercept method?

Determining the change in y using the gradient Signup and view all the answers

How is the steepness of the line represented in the equation $y = mx + c$?

By the coefficient $m$ Signup and view all the answers

Which point can be plotted directly from the equation $y = mx + c$ without additional calculations?

The y-intercept Signup and view all the answers

Which scenario describes the use of the dual intercept method?

Using both x-intercept and y-intercept to define the graph Signup and view all the answers

What does the variable $c$ represent in the equation $y = mx + c$?

The y-value when $x$ is zero Signup and view all the answers

What is the effect of increasing the value of $m$ in the equation $y = mx + c$?

It makes the graph slope upwards more steeply. Signup and view all the answers

If the equation of a line is given by $y = mx + c$ and $c < 0$, what can be said about the graph's behavior?

The graph will shift vertically downwards. Signup and view all the answers

What is the significance of the variable $c$ in the linear function $y = mx + c$?

It defines the y-intercept of the graph. Signup and view all the answers

For the linear function $f(x) = mx + c$, which of the following statements is true?

Both the domain and range encompass all real numbers. Signup and view all the answers

What does a negative value of $m$ indicate about the direction of the graph of $y = mx + c$?

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

To find the x-intercept of the line described by $y = mx + c$, which value should you set?

Set $y$ equal to $0$. Signup and view all the answers

If both $m$ and $c$ are positive, which description fits the graph of $y = mx + c$?

The graph slopes upwards and intersects the y-axis above the origin. Signup and view all the answers

Which of the following accurately describes the behavior of a line when $m = 0$ in the equation $y = mx + c$?

The line has no slope, resulting in a horizontal line. Signup and view all the answers

What impact does a positive gradient $m$ have on the general behavior of the graph of $y = mx + c$?

The graph will slope upward from left to right. Signup and view all the answers

How is the steepness of a line indicated when using the gradient and y-intercept method?

By the ratio of the vertical change to the horizontal change. Signup and view all the answers

What is the significance of calculating the x-intercept in the dual intercept method?

It provides a second point needed to sketch the line. Signup and view all the answers

If the function $f(x) = mx + c$ is plotted, where $m$ is zero, what can be inferred about the nature of the graph?

The graph will be a horizontal line at $y = c$. Signup and view all the answers

When identifying the x-intercept of the line represented by $y = mx + c$, which of the following equations must be resolved?

$0 = mx + c$ by setting $y$ to zero. Signup and view all the answers

What effect does a positive value of the constant $c$ have on the graph of the function $y = mx + c$?

The graph shifts vertically upwards. Signup and view all the answers

Which characteristic best describes the slope of the graph when $m$ equals zero in the function $y = mx + c$?

The graph is horizontal. Signup and view all the answers

In the equation $y = mx + c$, when $m$ is less than zero, how does the graph behave as $x$ increases?

The graph decreases in value. Signup and view all the answers

What can be inferred about the range of the function $f(x) = mx + c$?

The range consists of all possible real numbers. Signup and view all the answers

What is true about the y-intercept when the value of $c$ is zero in the function $y = mx + c$?

The graph crosses the y-axis at one point. Signup and view all the answers

How would the graph behave as $m$ approaches infinity in the equation $y = mx + c$?

The graph becomes steeper without bounds. Signup and view all the answers

If both variables $m$ and $c$ are negative in the equation $y = mx + c$, what is the likely shape of the graph?

The graph has a downward slope and may cross the y-axis. Signup and view all the answers

To graph the function $y = mx + c$, which point is calculated first if you are determining the x-intercept?

Set $y = 0$. Signup and view all the answers