The linear Function

Question 1

what is a graph of a straight line called

Answer 1

a linear function

Question 2

what is the standard form of a linear function

Answer 2

y = mx + c

Question 3

what is the x-intercept

Answer 3

the point where a graph cuts the x-axis

Question 4

what does the x and y-intercept mean

Answer 4

every point on the x-axis has a y-coordinate of 0 and every point on the y-axis has an x-coordinate of 0

Question 5

what is the y-intercept

Answer 5

the point where a graph cuts the y-axis

Question 6

to sketch a straight line, you one need two points

Question 7

how did the dual intercept method get its name

Answer 7

because the two points we choose are the intercepts with the two axis, which are calculated and plotted

Question 8

if a graph passes through the origin, the x- and y- intercepts will both be at the origin. substitute another value of x to determine the coordinates of a second point to draw a straight line.

Question 9

what is the gradient or slope of a line

Answer 9

the measure of the steepness of the line

Question 10

coefficient of x (m):
- determines the gradient of the graph
- if the gradients are equal, the the lines are parallel

Question 11

constant term (c):
- the y-value of the y-intercept
- y- intercept: (0;c)
- shifts the graph vertically up or down from the origin

Question 12

when is a line said to be increasing

Answer 12

if the y-values increase as the x-values increase

Question 13

what is the slope of an increasing line

Answer 13

slopes uphill from left to right

Question 14

when is a line said to be decreasing

Answer 14

if the y-values decrease as the x-values decrease

Question 15

how does a decreasing line slope

Answer 15

slopes downhill from left to right

Question 16

a) a graph with a positive gradient (m>0) is increasing
b) a graph with a negative gradient (m<0) is decreasing

Question 17

how do different values for m affect the gradient

Answer 17

if m is positive:
- the bigger the value of m, the steeper the slope of the graph
- the smaller the value of m, the more gradual the slop of the graph

if m is negative:
- the smaller the value of m, the steeper the slope of the graph
- the bigger the value of m, the more gradual the slope of the graph

Question 18

what is the formula for calculating gradient

Answer 18

m = change in y-values(vertical change) / corresponding change in x-values(horizontal change)

Question 19

parallel lines are lines that are always the same distance apart.
- || lines have equal gradients

Question 20

perpendicular lines are lines that meet or cross at a right angle
- if you multiply the gradients f perpendicular lines you always get -1
- to get the gradient of a perpendicular line, swap the numerator and denominator and change the sign

Question 21

what are the characteristics of vertical lines

Answer 21

• every point on the line has the same x-coordinate
• the line is parallel to the y-axis
• the gradient of the line is undefined

Question 22

what are the characteristics of horizontal lines

Answer 22

• every point on the line has the same y-coordinate
• the line is parallel to the x-axis
• the gradient of the line is zero

Question 23

read slides 39, 45

Question 24

what is a graph

Answer 24

a diagram showing the relationship between two quantities

Question 25

what does a constant horizontal graph show

Answer 25

That an increase in the value of the variable on the horizontal axis results in no change in the value of the variable on the vertical axis

Question 26

read through pg 267 the Cartesian plane

Question 27

how is the gradient or slope of a line measured

Answer 27

by the steepness of the line

Question 28

how is the rate of change calculated

Answer 28

by the amount by which the output variable changes when the input variable is increased by 1

Question 29

m = change in y/ change in x