A linear relationship is any equation that, when graphed, gives you a straight line. A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain in the same linear function condition. This overview is like a linear relationships study guide for teachers.
The equation can have up to two variables, but it cannot have more than two variables.
All the variables in the equation are to the first power. None are squared or cubed or taken to any power. And also, none of the variables will be in the denominator.
The equation must be graphed as a straight line. Linear relationships such as y = 2 and y = x all graph out as straight lines. When graphing y = 2, you get a line going horizontally at the 2 mark on the y-axis. When graphing y = x, you get a diagonal line crossing the origin.
The expression for the linear equation is; y = mx + c
Linear relationship Example
1.Let’s draw a graph for the following function:
F(2) = -4 and f(5) = -3
·Let’s rewrite it as ordered pairs(two of them).
·f(2) =-4 and f(5) = -3
·(2, -4) (5, -3)
2.Find the slope of a graph for the following function.
f(3) = -1 and f(-8) = -6
·Let’s write it again as ordered pairs
·f(3) =-1 and f(8) = -6
·(3, -1) (8, -6)
·we will use the slope formula to evaluate the slope
·(3, -1) (8, -6)
·(x1 , y1) (x2 , y2)
·Slope Formula, m =y2−y1/x2−x1
·m = 1 is the slope for this function.
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Linear relationships can give insight into how variables interact with one another. Linear relationships can support statistical analysis to determine the presence of correlations and causal relationships between variables.
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