Understanding Linear Functions and Graphs

• 5

• -3

• 3

• 0

Answer explanation

The y-intercept of a linear equation is the value of y when x = 0. In the equation y = 5x - 3, substituting x = 0 gives y = -3. Therefore, the y-intercept is -3.

• -2

• 7

• 2

• -7

Answer explanation

In the equation y = -2x + 7, the slope is the coefficient of x. Here, the coefficient is -2, which indicates the slope of the linear function. Therefore, the correct answer is -2.

Which of the following equations is not a linear function?

Answer explanation

The equation y = x^2 + 1 is not a linear function because it contains the term x^2, which makes it a quadratic function. The other equations are linear as they can be represented in the form y = mx + b.

• 3

• 9

• -3

• -9

Answer explanation

To find the y-intercept, set x = 0 in the equation 3x + y = 9. This gives y = 9. Therefore, the y-intercept is 9.

A catering company charges a fixed fee and an additional charge per person.

If I were to rewrite this situation in slope intercept form y=mx+b

The fixed fee represents the: ​ (a)   ​

• y-intercept

• slope

Answer explanation

In the equation y=mx+b, the fixed fee corresponds to the y-intercept (b). It represents the initial cost before any additional charges per person (the slope, m) are added.

In slope-intercept form, y = mx + b, the m stand for the ​ ​ (a)  

and the b stands for the ​ (b)  

• slope

• y-intercept

• x-intercept

Answer explanation

In the slope-intercept form y = mx + b, 'm' represents the slope of the line, indicating its steepness, while 'b' represents the y-intercept, the point where the line crosses the y-axis.

What does "m" represent in y=mx+b?

• y-intercept

• slope

• macaroni

• nothing

Answer explanation

In the equation y=mx+b, 'm' represents the slope of the line. It indicates how steep the line is and the direction it goes. The correct answer is 'slope', not y-intercept, macaroni, or nothing.

Which graph can be defined by the function y = -3x + 2?

(a)  

• Graph A

• Graph B

• Graph C

• Graph D

Answer explanation

The function y = -3x + 2 is a linear equation with a slope of -3 and a y-intercept of 2. Graph B correctly represents this line, showing a downward slope starting at (0, 2).

Consider the following equation: y = 50x + 75

Nadia is buying concert tickets for herself and her friends. She will pay ​ (a)   for each ticket plus a one-time online fee of ​ (b)   .

• $50

• $75

• $25

• $125

Answer explanation

In the equation y = 50x + 75, the coefficient of x (50) represents the cost per ticket, and the constant (75) represents the one-time fee. Thus, Nadia pays $50 for each ticket and a $75 fee.

Identify the slope of the following graph.

• Positive

• Negative

• Zero

• Undefined

Answer explanation

The slope of a graph indicates its steepness and direction. A positive slope means the graph rises as it moves from left to right, confirming that the correct answer is 'Positive'.