4.09 Graphing lines
For each of the following graphs:
State the slope of the line.
State the y-intercept.
Write the equation of the line in slope-intercept form.
Sketch the graph of the following lines given the y-intercept and slope:
A y-intercept of 2 and slope of - \dfrac{5}{4}.
A y-intercept of - 3 and slope of - \dfrac{2}{5}.
A y-intercept of 7 and slope of - \dfrac{3}{4}.
A y-intercept of - 2 and slope of 5
A y-intercept of - 2 and slope of \dfrac{1}{2}
A y-intercept of 2 and slope of \dfrac{1}{2}
A y-intercept of 7 and slope of - 1
A y-intercept of - 3 and slope of \dfrac{1}{2}
Sketch the graph of the following linear equations:
y = x + 1
y = 3 x - 1
y = - x + 4
y = 4 x-1
y = - 3 x - 4
y = 3 x + 1
y = \dfrac{1}{2} x - 2
y = \dfrac{x}{3} + 3
Consider the following three linear equations and their corresponding graphs:
y = x + 4, \, y = 2 x + 4, \, y = 4 x + 4
What do all of the equations have in common?
What do all of the graphs have in common?
What conclusion can be made about lines that have the form y = m x + 4?
Consider the following three linear equations and their corresponding graphs:
y = 2x + 2, \, y = 2 x + 4, \, y = 2 x -1
What do all of the equations have in common?
What do all of the graphs have in common?
What conclusion can be made about lines that have the form y = 2 x + b?
The table shows some points on the line with equation x = 0.
Does the line x = 0 represent the y-axis or x-axis?
| x | 0 | 0 | 0 | 0 |
|---|---|---|---|---|
| y | -8 | -1 | 4 | 6 |
The table shows some points on the line with equation y = 0.
Does the line y = 0 represent the y-axis or x-axis?
| x | -6 | -4 | 1 | 5 |
|---|---|---|---|---|
| y | 0 | 0 | 0 | 0 |
Consider the sets of points in the following coordinate planes:
State whether the set of points lies on an increasing, decreasing, vertical or horizontal line.
Find the equation of the line that passes through the set of points.
Explain why the slope of a vertical line is undefined.
If the slope of a line is zero, what does this tell us about the line?
Determine whether the graph of the following equations are horizontal or vertical lines:
y = 6
x = - 4
x = 0
y = 0
y = -10
x = \dfrac{1}{2}
y = \dfrac{4}{5}
x = 1.5
Sketch the graph of the following linear equations:
x = 4
y = - 4
x = - 3
y = 1
y = \dfrac{1}{2}
x = -\dfrac{1}{4}
y = -10
x = 12