Advanced I Patterns, Relations, and Algebra, linear relations (7-9 old curriculum that was not addressed by 5-6 new; concepts extend into math 10C)) Flashcards
What is the equation of a line? What is a linear equation?
Equation of a line is the same thing as a linear equation.
y = mx + b
m is the slope
b is the y-intercept
x and y are variables that allow you to put in one of them such as x, and return the other, such as y
Typically the slope and y-intercept are already known so you will have an equation such as:
y = 2x +5 where 2 is the slope and 5 is the y-intercept
If you know two points are on the line, then you can sub in the points (x,y) and another (x,y) into the equation, and solve for the variables m and b.
In another situation you may know the slope and one point (x,y) and this can allow you to find the variables m and b as well.
So the equation of a line can be determined from two points on the line, or a point and the slope.
This is where you will need to memorize y=mx + b in order to make that equation.
Remember that a table of values will only need two rows in order for you to determine the equation, provided that the equation is of a line.
Equations of lines will not have powers on the variable x or y, so make sure that you have determined that you actually have a line before you use any of the above techniques.
What is the slope?
Represented by m in the equation of a line, the slope is equal to the change in y from one point to the next, divided by the change in x for those same two points.
slope = m = rise/run = change in y / change in x
slope is the thing that is multiplied by the independent variable which is usually x
slope is how much you go up for every one unit of movement to the right
slope can be found in the linear equation:
y = mx + b
What is the y-intercept?
y-intercept means where the graph (in this grade where the line) meets the y-axis. If you set x = 0, then it will return a y-value. The y-value at x=0 is the y-intercept.
For example in y = 2x + 5 we have a y-intercept that can be found by subbing in x = 0:
y = 2x + 5
y = 2(0) + 5
y = 5
so when x = 0, y = 5
Thus the y-intercept is (0,5) or sometimes people will just say “5” rather than the coordinate point since we already know from context that they are referring to the y-intercept and thus x = 0 by definition of the y-intercept.
in the linear equation y= mx + b you will notice that b is always equal to the y-intercept.
What is an inequality and how do you solve them compared to regular equations?
If you must divide or multiply by a negative you must switch the direction of the inequality sign. This is usually not done since there are ways of solving that allow you to work around needing to work with negatives in this way, but watch out for it since it can occur.
What does it mean to interpolate?
What does it mean to extrapolate?
interpolate: use points on either side of where you are looking to get data to predict the value between
extrapolate: continue the pattern or line on a graph to see what values could be outside of the domain of your data (so farther out than your farthest points)
