A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. A linear equation is special because:
A linear equation in one unknown x may always be rewritten
If a≠0, there is a unique solution
If a = 0, then either the equation does not have any solution, if b ≠ 0 (it is inconsistent), or every number is a solution, if b is also zero.
A common form of a linear equation in the two variables x and y is Y=mx+b
where m and b designate constants (parameters). The constant m determines the slope or gradient of that line and the constant term b determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.
Let's draw the graph of this equation.
y = 1/2 x+ 2
We can start with any two x values we like and then find y for each x by substituting the x values into the equation. Let's start with x = 1.
|Value of x||y=1/2 x +2||Value of y|
Let's plot these points and draw a line through them.
Slope: The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:
y = a + bx
b is the slope
a is a constant term. It is the y intercept, the place where the line crosses the y axis.
y = -13 + 7x
This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.