Consider the following graphs of the equations y = x + 3, y = 2 x + 3 and \\y = 4 x + 3:
What is the same about all three equations?
What is the same about all three lines?
What can be concluded about the constants in equations and the y-intercepts of their graphs?
What does the following stand for in the equation of a line: y = mx + c?
State the y-intercept of the line y = - x + 6.
For each of the following equations:
State the y-intercept.
State the gradient.
For each of the following lines:
State the y-intercept.
Find the gradient.
For each of the following lines:
State the gradient.
State the y-intercept.
Find the equation of the line in gradient-intercept form.
Find the equation of the following lines:
Consider the following table of values:
| x | -2 | 0 | 2 | 4 |
|---|---|---|---|---|
| y | 6 | 4 | 2 | 0 |
Graph the line going through these points.
Write the equation of the line that goes through these points.
Write the equation of the following lines in gradient-intercept form:
A line that has a gradient of - 3 and crosses the y-axis at 1.
A line that has a gradient of 2 and a y-intercept of - 5.
A line that has a gradient of \dfrac{2}{3} and passes through the point \left(0, 3\right).
A line that has a gradient of \dfrac{3}{4}, and intersects the y -axis at - 1.
A line that has the same gradient as y = 7 - 3 x and the same y-intercept as \\ y = - 7 x - 8.
Sketch the graph of a line with y-intercept of - 2 and gradient of 5.
Sketch the graph of the following linear equations:
y = - 4 x + 4
y = 2 x-1
y = 4 x + 3
y = 4 x - 1
Determine whether the following lines pass through the origin \left(0 , 0\right):
y = 6 x
y = \dfrac{x}{6}
y = 6 x - 6
y = 8 x + 8
y = 8 x
State the equation of the following graphed lines:
Sketch the following lines on a number plane:
Consider the given table for the linear equation y = 0:
Does this represent the y-axis or x-axis?
| x | 4.5 | 0.5 | 3.5 | 8.5 |
|---|---|---|---|---|
| y | 0 | 0 | 0 | 0 |
Consider the given table for the linear equation x = 0:
Does this represent the y-axis or x-axis?
| x | 0 | 0 | 0 | 0 |
|---|---|---|---|---|
| y | - 5.5 | - 2.5 | 3.5 | 6.5 |
State the point of intersection of the following pairs of lines:
x = 6 and y = - 3
x = 1 and y = 5
x = -2 and y = - 1
x = 0 and y = 8
A cleaner charges a callout fee of \$90 plus \$30 per hour.
Write an equation to represent the total amount charged, y, by the cleaner as a function of the number of hours worked, x.
Sketch the graph of y against x for 0 \leq x \leq 6.
State the gradient of the line.
State the y-intercept.
Robert is running a 80 \text{ km} ultramarathon at an average speed of 15 \text{ km/h}.
Write an equation to represent the distance Robert has left to run, y, as a function of the number of hours since the start, x.
Sketch the graph of y against x for 0 \leq x \leq 6.
State the gradient of the line.
State the y-intercept.
Mario is running a 100 \text{ km} ultramarathon at an average speed of 9 \text{ km/h}.
Write an equation to represent the distance Mario has left to run, y, as a function of the number of hours since the start, x.
State the gradient of the function.
Describe what the gradient of the line represents in context.
State the y-intercept.
Describe what the y-intercept represents in context.
Find the distance Mario will have left to run after 4.5 hours.