1.2 Graphs and Lines Flashcards
The fundamental theorem of analytic geometry.
There is a one-to-one correspondence between the points in a plane and the elements in the set of all ordered pairs of real numbers.
What is a linear equation in one variable?
We called an equation of the form
ax +b=0 (a cannot equal 0)
a linear equation in one variable
Standard form of a linear equation in Two Variables
What is a solution of an eqqquation in two variables?
A solution of an equation in two variables is an ordered pair of real numbers that satisfies the equation. For example, 14, 32 is a solution of 3x -2y =6.
What is a the solution set of an equation in two variables?
The solution set of an equation in two variables is the set of all solutions of the equation.
Theorem 1: Graph of a linear Equation in two variables.
If A and B are not 0, or if A = 0 and B does not, or if B is 0 and A is not, what are they different ways you can write the equation of a line in the form of Ax + By = C
What is the x and y intercept?
The y intercept is the y coordinate of the point where the graph crosses the y axis.
The x intercept is the x coordinate of the point where the graph crosses the x axis.
How can you find the x and y intercepts?
To find the y intercept, let x =0 and solve for y.
To find the x intercept, let y =0 and solve for x.
It is a good idea to find a third point as a check point.
Definiton of the slope of a line.
What is the slope-intercept form ofa line?
y = mx+b
What is point-slope form?
Why is the point slope form useful?
The point-slope form is extremely useful, since it enables us to find an equation for a line if we know its slope and the coordinates of a point on the line or if we know the coordinates of two points on the line.
When the slope of a line is undefined, how do we write the standard form? is there a point - intercept form?
x = a
Where a is the x coordinate of each point.
There is no point-intercept form when the slope is undefined.
