13.11 Graphs of linear equations
For each of the following graphs:
State the value of the x-intercept.
State the value of the y-intercept.
Given each linear equation and its graph, state the coordinates of the y-intercept:
Consider the following graph of the line y = - 2 x + 3:
State the the y-value, when x is 0.
Explain the relationship between the value of the y-intercept and the equation of the line.
If the equation of a line is y = m x + c, state the value of the y-intercept.
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?
Find the value of the y-intercept of the following lines:
y = 7 x + 3
y = 3 x - 5
y = - 8 x - 3
y = - 8 x + 4
y = 9 x
y = 2
y = 2x+\dfrac{2}{3}
y = \dfrac {3 x + 8}{5}
Determine whether the following equations represent lines that will cross the y-axis at 2:
y = 5 x + 2
y = 2 - x
y = 2 x
y = 2 x - 4
y = x + 2
y = x - 2
y = 2
y = \dfrac{x + 4}{2}
The x-intercept occurs when y=0. Find the value of the x-intercept for the following lines:
y = 2 x - 2
3x + y = -3
y = 4 x - 8
2y + x = -3
y = 9 x
2y + 2x = 4
3x - 5y = 1
x = \dfrac {3 y + 10}{5}
For each of the following equations:
Find the coordinates of the y-intercept.
Find the coordinates of the x-intercept.
Use the intercepts to sketch the graph of the line.
y = 2 x - 4
y = - 2 x + 2
y = 3 x - 3
y = - 4 x + 8
Consider the linear equation y = 5 x .
Find the coordinates of the y-intercept.
Find the coordinates of the x-intercept.
Find the value of y when x = 2.
Hence, sketch the graph of the line.
Consider the linear equation y = - \dfrac {5 x}{4}.
Find the coordinates of the y-intercept.
Find the coordinates of the point on the line where x = 4.
Hence, sketch the graph of the line.
If a line has equation y=mx + c, explain how you can tell if the line will pass through the origin.
Determine whether the following equations represent lines that will pass through the origin:
y = 8 x - 8
y = \dfrac {x}{8}
y = - 6 x
y = 8 x
y = \dfrac {x}{8}
y = 0
y = - x
y = - 6 x - 6
Consider the line graph shown:
State the y-value when x=0.
State the y-value when x=1.
When the x-value increases by 1, by how much does the y-value change?
Hence state the gradient of the line, m.
The equation of this line is y = 2 x + 4. Explain how to find the gradient from the equation of the line.
Consider the following three linear equations and their corresponding graphs:
y = 4 x + 3, \, y = 4 x + 6, \, y = 4 x - 3
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 = 4 x + c?
Find the gradient, m, of the following linear equations:
y = 9 x + 3
y = - 7 x + 5
y = \dfrac{5x}{4} + 2
y = -x + 5
From the following list of equations, select the lines that have the same gradient:
-
y = 2 + 7 x
-
y = \dfrac {x}{7} + 2
-
y = 5 - 7 x
-
y = 7 x
y = 5 x + 7
y = 7 x - 2
For each linear equation:
Find the value, m, of the gradient.
Find the value, c, of the y-intercept.
y = 2 x + 9
y = 5 x - 6
y = - 5 x + 8
y = - 4 x - 2
2y = 8 x - 1
3y = -6 x - 2
y - 5x = 4
2y - 3x = 6
Given the values of m and c, write the equation of the line:
m=2, c= 5
m=-3, c= 2
m=-2, c= -1
m=4, c= 0
m=0, c= -7
m=0, c= 4
m=\dfrac{1}{2}, c= -2
m=-\dfrac{3}{4}, c= \dfrac{1}{2}
Approximate the solutions of the following equations using the graphs provided. Round your answers to one decimal place.
Consider the following graph of the line y = - 3 x + 7:
Estimate the x-intercept to one decimal place.
Hence, estimate the solution to the equation - 3 x + 7=0 to one decimal place.
Estimate the x-coordinate of the point on the line where y=6.
Hence, estimate the solution to the equation - 3 x + 7=6 to one decimal place.
Estimate the solutions of the following equations by first drawing the appropriate graph. Round your answers to one decimal place.