For the following graphs:
State the value of the x-intercept.
State the value of the y-intercept.
For each of the following tables of values:
Find the gradient, m.
Find the y-intercept, c.
Write the equation of the line expressing the relationship between x and y.
Complete the table of values.
| x | 0 | 1 | 2 | 3 | 4 | 24 |
|---|---|---|---|---|---|---|
| y | 0 | 4 | 8 | 12 | 16 |
| x | 0 | 1 | 2 | 3 | 4 | 21 |
|---|---|---|---|---|---|---|
| y | 9 | 14 | 19 | 24 | 29 |
| x | 0 | 1 | 2 | 3 | 4 | 25 |
|---|---|---|---|---|---|---|
| y | - 23 | - 21 | - 19 | - 17 | - 15 |
| x | 0 | 1 | 2 | 3 | 4 | 70 |
|---|---|---|---|---|---|---|
| y | 27 | 22 | 17 | 12 | 7 |
For each of the following tables of values:
Find the equation of the line expressing the relationship between x and y.
Complete the table of values.
| x | 1 | 2 | 3 | 4 | 19 |
|---|---|---|---|---|---|
| y | 5 | 10 | 15 | 20 |
| x | 1 | 2 | 3 | 4 | 16 |
|---|---|---|---|---|---|
| y | - 3 | - 6 | - 9 | - 6 |
| x | 1 | 2 | 3 | 4 | 60 |
|---|---|---|---|---|---|
| y | 1 | 4 | 7 | 10 |
| x | 1 | 2 | 3 | 4 | 80 |
|---|---|---|---|---|---|
| y | - 14 | - 22 | - 30 | - 38 |
| x | 1 | 2 | 3 | 4 | -15 |
|---|---|---|---|---|---|
| y | 82 | 74 | 66 | 58 |
Find the equation that corresponds to each of the following tables:
| x | - 1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|
| y | 7 | 4 | 1 | - 2 | - 5 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 5 | 8 | 11 | 14 | 17 |
| x | - 8 | - 7 | - 6 | - 5 | - 4 |
|---|---|---|---|---|---|
| y | - 37 | - 32 | - 27 | - 22 | - 17 |
| x | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| y | -1 | - 3 | - 5 | - 7 | - 9 |
Find the equation of the following lines:
A line that passes through the point A \left( - 5 , - 4 \right) and has a gradient of - 4.
A line that passes through the point A \left( - \dfrac{4}{5} , - 4 \right) and has a gradient of 2.
A line that passes through Point A \left( - 4 , 3\right) and has a gradient of 4.
A line that passes through Point A \left(7, - 6 \right) and has a gradient of - 3.
A line that passes through the point A \left(3, 5\right) and has a gradient of - \dfrac{5}{2}.
A line that passes through the point A \left(4, 3\right) and has a gradient of - 3\dfrac{1}{3}.
A line that passes through the point A \left( - 4 , 3\right) and has a gradient of - 9.
A line that passes through the point A \left( - \dfrac{5}{9} , 7\right) and has a gradient of 7.
A line that passes through the point A \left(8, 1\right), and has a gradient of \dfrac{5}{2}.
A line that passes through the point A \left( - 4 , 5\right) and has a gradient of 3\dfrac{1}{2}.
For each of the following lines:
Find the equation of the line.
Sketch the graph of the line.
A line has gradient 2 and passes through the point \left( - 5 , - 3 \right).
A line has gradient - \dfrac{3}{2} and passes through the point (- 2, 2).
A line has gradient - \dfrac{2}{5} and passes through the point \left( - 10 , 2\right).
A line has gradient - 3 and passes through the point \left(2, - 12 \right).
Consider the line with equation 2 x + y - 8 = 0.
Find the x-intercept of the line.
Hence, find the equation of a line with a gradient of - 4 that passes through the x-intercept of the given line.
Find, in general form, the equation of a line which has a gradient of \dfrac{4}{7} and cuts the x-axis at - 10.
For each of the following lines:
Find the gradient of the line.
Find the equation of the line.
A line passes through the points \left(2, - 7 \right) and \left( - 5 , 6\right).
A line passes through the points \left(3, - 3 \right) and \left(5, - 11 \right).
A line passes through the points A \left( - 6 , 7\right) and B \left( - 8 , - 4 \right).
Identify which of the following equations of straight lines have a gradient of 5 and pass through the point A \left(-1, - 4 \right):
\dfrac{y + 4}{x + 1} = 5
\dfrac{x + 1}{y + 4} = 5
\dfrac{- 4 - y}{-1 - x} = 5
\dfrac{y + 1}{x + 4} = 5
Write down the equations of three lines that pass through the point (1, 3). Explain how your lines are different.
Find the equation of the following lines:
A line that is parallel to the x-axis and passes through \left( - 10 , 2\right).
A line that is parallel to the y-axis and passes through \left( - 7 , 2\right).
A line that is parallel to the line y = - 3 x - 8 and cuts the y-axis at - 4.
A line goes through A \left(3, 2\right) and B \left( - 2 , 4\right):
Find the gradient of the given line.
Find the equation of another line that has a y-intercept of 1 and is parallel to this line.
Consider line L_1 with equation: 5 x - 4 y + 2 = 0.
Find the gradient of a line, L_2, that is parallel to L_1.
Find the equation of L_2 using the point-gradient formula, given that it passes through Point A \left( - 4 , 6\right). Express the equation in general form.
Find the equation of the following lines:
Passes through the point \left(9, - 5 \right) and is parallel to the line y = - 5 x + 2.
Passes through the point \left(-2, -4\right) and is parallel to the line y = 2x+13.
Passes through the point \left(10, 6\right) and is parallel to the line y = -6x-4.
Passes through the point \left(-3, 7\right) and is parallel to the line y = -12x+5.
A line has a gradient of \dfrac{3}{10} and passes through the midpoint of A \left( - 6 , - 6 \right) and B \left(8, 8\right).
Find the coordinates of M, the midpoint of AB.
Find the equation of the line in general form.
Consider the lines L_{1}, y = - 4 x + 5, and L_{2}, y = x - 1.
Find the midpoint M of their y-intercepts.
Find the equation of the line that goes through the point M and has gradient \dfrac{1}{3}. Express the equation in general form.
A circle with centre C \left(11, 13\right) has a diameter with end points A \left(5, 14\right) and B \left(p, q\right).
Find the value of p.
Find the value of q.
Find the equation of the line passing through B with gradient \dfrac{9}{2}.