Slope and y-intercept
Examine the graphs from the graphing activity we just completed. Which relationships are linear
relationships?
1. Complete the table below.
Graph
Equation
Linear or Non-Linear?
A
B
C
D
E
F
G
2. Can you make a statement that describes how one can tell if a relationship is linear simply by examining
its equation?
3. Examine the equations below. Which equations represent linear relationships?
𝑦 = 4𝑥 − 16
𝑦 = 𝑥 3 − 3𝑥
1
4
𝑦 = 𝑥+9
We describe lines by their slope and y-intercept.
Slope – a measure of “steepness”
y-intercept – place where a graph crosses the y-axis
𝑦 = 2𝑥 2 − 3
𝑦=
1
𝑥
Slope is defined by the ratio
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
. Slope can be found between any 2 points on a line,
and will always be the same (regardless of points chosen).
4. Find the slope of each line below.
5. The y-intercept is the point where the graph crosses the y-axis. Find the y-intercept for each graph
above.
6. Find the slope of the line that passes through the points (-3, 3) and (1, -5)
7. a) Find the slope and y-intercept for the graph below.
b) what does the slope represent?
c) What does the y-intercept represent?
8.
a) Find the slope and y-intercept for this
graph.
b) What does the slope represent?
c) What does the y-intercept represent?
9. Sketch a line with a y-intercept of -3 and a slope of
4 and a slope of -2.
2
. Then sketch a second line with a y-intercept of
3