The linear Function Flashcards
what is a graph of a straight line called
a linear function
what is the standard form of a linear function
y = mx + c
what is the x-intercept
the point where a graph cuts the x-axis
what does the x and y-intercept mean
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
what is the y-intercept
the point where a graph cuts the y-axis
to sketch a straight line, you one need two points
how did the dual intercept method get its name
because the two points we choose are the intercepts with the two axis, which are calculated and plotted
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.
what is the gradient or slope of a line
the measure of the steepness of the line
coefficient of x (m):
- determines the gradient of the graph
- if the gradients are equal, the the lines are parallel
constant term (c):
- the y-value of the y-intercept
- y- intercept: (0;c)
- shifts the graph vertically up or down from the origin
when is a line said to be increasing
if the y-values increase as the x-values increase
what is the slope of an increasing line
slopes uphill from left to right
when is a line said to be decreasing
if the y-values decrease as the x-values decrease
how does a decreasing line slope
slopes downhill from left to right
a) a graph with a positive gradient (m>0) is increasing
b) a graph with a negative gradient (m<0) is decreasing
how do different values for m affect the gradient
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
what is the formula for calculating gradient
m = change in y-values(vertical change) / corresponding change in x-values(horizontal change)
parallel lines are lines that are always the same distance apart.
- || lines have equal gradients
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
what are the characteristics of vertical lines
- 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
what are the characteristics of horizontal lines
- 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
read slides 39, 45
what is a graph
a diagram showing the relationship between two quantities
what does a constant horizontal graph show
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
read through pg 267 the Cartesian plane
how is the gradient or slope of a line measured
by the steepness of the line
how is the rate of change calculated
by the amount by which the output variable changes when the input variable is increased by 1
m = change in y/ change in x
