Straight Line Equations and Inequalities
Straight Line Equations and Inequalities
A: Linear Equations - Straight lines
Please remember that when you are drawing graphs you should always label your axes and that y is always shown on the vertical axis. A linear equation between two variables x and y can be represented by y = a + bx where “a” and “b” are any two constants. For example, suppose we wish to plot the straight line If x = -2, say, then y = 3 + 2(-2) = 3 - 4 = -1 If x= -2 -1 -1 1 0 3 1 5 2 7 As you can see, we have plotted the five points on the graph. They do indeed all lie on a straight line and we have joined them together to show the line. Of course, you could draw the line by just plotting any two points on it and then joining and extending those two points. y = 3 + 2x ..... and so on (see table below)
Then y =
y
x
The equation simply represents the relationship between two variables x and y. For example: suppose our basic salary is £4000 and we add commission to that at the rate of 5% of our total sales. Call y our total salary and call x our sales (both in £) then we could represent this relationship as y = 4000 + 0.05x (5% is five hundredths i.e. 0.05) Then, if we knew that total sales were 6000, we could work out total salary: y = 4000+0.05(6000) or £4300
For our next example, we will draw the equation y = 6 - x on a graph (using just two points): For y = 6 - x Put x = 1 then y = 6 - 1 = 5 Put x = 4 then y = 6 - 4 = 2
Page 1
y
Y=6 - X
Plot the two points x=1, y=5 x=4, y=2 on the graph ... and then join and extend. We have now drawn the line. See the exercise below. x
EXERCISE 1: Draw the following on the same graph: y = 1 + 4x and y = 6 - 2x
B: Simultaneous Equations
When we have two linear equations in two variables, say x and y, then we can often find a “unique solution” for these equations. That is, we can often find a value for x and a value for y which “satisfies” both equations simultaneously. On a graph, it is the point where the two lines
A: Linear Equations - Straight lines
Please remember that when you are drawing graphs you should always label your axes and that y is always shown on the vertical axis. A linear equation between two variables x and y can be represented by y = a + bx where “a” and “b” are any two constants. For example, suppose we wish to plot the straight line If x = -2, say, then y = 3 + 2(-2) = 3 - 4 = -1 If x= -2 -1 -1 1 0 3 1 5 2 7 As you can see, we have plotted the five points on the graph. They do indeed all lie on a straight line and we have joined them together to show the line. Of course, you could draw the line by just plotting any two points on it and then joining and extending those two points. y = 3 + 2x ..... and so on (see table below)
Then y =
y
x
The equation simply represents the relationship between two variables x and y. For example: suppose our basic salary is £4000 and we add commission to that at the rate of 5% of our total sales. Call y our total salary and call x our sales (both in £) then we could represent this relationship as y = 4000 + 0.05x (5% is five hundredths i.e. 0.05) Then, if we knew that total sales were 6000, we could work out total salary: y = 4000+0.05(6000) or £4300
For our next example, we will draw the equation y = 6 - x on a graph (using just two points): For y = 6 - x Put x = 1 then y = 6 - 1 = 5 Put x = 4 then y = 6 - 4 = 2
Page 1
y
Y=6 - X
Plot the two points x=1, y=5 x=4, y=2 on the graph ... and then join and extend. We have now drawn the line. See the exercise below. x
EXERCISE 1: Draw the following on the same graph: y = 1 + 4x and y = 6 - 2x
B: Simultaneous Equations
When we have two linear equations in two variables, say x and y, then we can often find a “unique solution” for these equations. That is, we can often find a value for x and a value for y which “satisfies” both equations simultaneously. On a graph, it is the point where the two lines