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Yes, the graph of a linear equation can be a line.
There are special cases, sometimes trivial ones like y=y or x=x which are linear equations, but the graph is the entire xy plane.
The point being, linear equations most often from a line, but there are cases where they do not.
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Where the given equations are not linear?
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
How are linear equations similar or different from functions?
A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.
When writing linear equations how do you determine which form of a line to use?
It does not matter because they are equivalent. You can always convert from a slope-intercept form to a standard linear form (and vice versa).
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
Where the given equations are not linear?
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
How are linear equations similar or different from functions?
A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.
When writing linear equations how do you determine which form of a line to use?
It does not matter because they are equivalent. You can always convert from a slope-intercept form to a standard linear form (and vice versa).
Why is linear equations called linear equations?
Because its linear and the equation is a problem to solve
Why are linear equations infinite?
When you graph a linear equation, you make a line. A line continues infinitely.
Linear and nonlinear equations?
A linear equation is, basically, a line. An example is y=2x+3. They are commonly found in the form y=mx+b where m is the slope, and b is the y-intercept (where the line crosses the y-axis). A non-linear equation can be many things. Parabolas and exponential equations are not linear.
Why can all linear equations that describe functions be written in point slope form?
Because a linear equation is, by definition, a straight line. Any line can be defined by selecting any one point on the line and the slope of the line.
What is a system of linear equations?
A system of linear equations determines a line on the xy-plane. The solution to a linear set must satisfy all equations. The solution set is the intersection of x and y, and is either a line, a single point, or the empty set.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
What are the importance of linear equation?
They are the simplest form of relationship between two variables. Non-linear equations are often converted - by transforming variables - to linear equations.
What are inifintly equations?
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
