4.08 Identifying slope and y-intercept
State the term used to describe the change in the horizontal distance along a line.
State the definiton of the slope of a line.
Write the formula for slope in terms of the vertical rise and the horizontal run.
Explain what it means if the slope of a line is undefined.
Explain what it means if the slope of a line is zero.
Consider the following graph:
Find the slope of the line.
Find the slope of each of the following line segments between points A and B:
A \left( - 4 , 0\right) and B \left( 0 , 2\right)
A \left( 1, 0\right) and B \left( 0 , 4\right)
A \left( 5 , 3\right) and B \left( -5 , 2\right)
A \left( 0 , 3\right) and B \left( 3 , 5\right)
A \left( 2 , -1\right) and B \left( -1 , 5\right)
A \left( - 4 , 2\right) and B \left( 2 , 5\right)
A \left( 4 , -1\right) and B \left( 8 , -4\right)
A \left( 5, -1\right) and B \left( -5 , 1\right)
Find the slope of the line that passes through the following points:
\left(3, 4\right) and \left(5, 4\right)
\left( - 3 , 4\right) and \left(1, 4\right)
\left( - 1 , 0\right) and \left(0, 3\right)
\left(1, - 4 \right) and the origin
\left(2, - 6 \right) and the origin
\left( - 6 , 5\right) and \left(4, 5\right)
\left( - 2 , - 5 \right) and \left( - 9 , - 12 \right)
\left( - 3 , - 1 \right) and \left( - 5 , 1\right)
\left(4, 1\right) and \left(11, - 6 \right)
\left(0, - 4 \right) and \left(5, -1\right)
\left( - 7 , - 6 \right) and \left( - 5 , - 8 \right)
\left(4, 0\right) and \left(0, 16\right)
State what the following variables stand for in the equation of a line y = mx + b:
For each of the following equations:
State the slope of the line.
State the y-intercept of the line.
Find the slope of the line y = \dfrac{9 - x}{2}.
Consider the equation of a line: y = 4 \left( 4 x - 3\right)
Rewrite equation in the form y = m x + b.
State the slope of the line.
State the y-intercept of the line.
Consider the following graph:
State the slope of the line.
State the y-intercept of the line.
Does this line have an x-intercept?
Consider the following graph:
State the slope of the line.
Does this line have a y-intercept?
State the x-intercept of the line.
Consider the table of values for the equation y = x:
Plot the points in the table of values.
Find the coordinates of the y-intercept.
Find the slope of the line.
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | -1 | 0 | 1 | 2 |
Given points P\left(- 1,-1\right), Q\left(0,1\right), R\left(- 1,6\right), and S\left(- 2, 4\right):
Find the slope of PQ.
Find the slope of RS.
Find the slope of QR.
Find the slope of PS.
What type of quadrilateral is PQRS? Explain your answer.
Consider the ramp shown in the diagram:
Find the slope of this skateboard ramp if it rises 0.9 \text{ yd} above the ground and runs 1 \text{ yd} horizontally at the base.
The ramp can only be used as a 'beginner’s ramp' if for every 1 \text{ yd} horizontal run, it has a rise of at most 0.5 \text{ yd}. Can it be used as a 'beginner’s ramp'?
A certain ski resort has two ski runs as shown in the diagram:
Find the slope of Run A, correct to two decimal places.
Find the slope of Run B, correct to two decimal places.
Which run is steeper?
