7th Grade Chapter 8
8-1 Relations and Functions
You can think of a function as a number generator. If you input one number into the function, the function outputs a second number. The first coordinate in each ordered pair is the input number, a member of the domain. The second coordinate in each ordered pair is an output number, a member of the range.
8-2 Equations with Two Variables
The coordinates of every point on a line in a coordinate plane make the equation of the line a true statement. Since a line has infinite length, a linear equation has an infinite number of solutions. Any equation that can be written inthe form y-mx+b is a linear function whose graph is a line. So y=3, where m=0 and b=3, is a linear function. However, the equation x=3 is not a function. It is a vertical line and therefore does not pass the vertical-line test.
8-3 Slope and y-intercept
A formula for the slope of a non-vertical line is m = (y2-y1)/(x2-x1), where m is the slope and  (x1,y1) and (x2,y2) are two points on the line. You may choose any two points on the line to calculate the slope.
8-4 Direct Variation
A direct variation is a liner function of the form y=kx, where k does not = 0. It can be expressed as “y varies directly with x”. For all solutions of y=kx, where k doesn’t = 0 and x doesn’t equal zero, the ratio y/x is always the same; it equals k, the constant of variation, which is also the slope.
8-6 Solving Systems of Linear Equations
Any two nonparallel lines on a coordinate plane intersect. The coordinates of the point of intersection form a solution of the equations for both lines.
8-7 Linear Inequalities
A system of linear equations whose graphs intersect in one point has only one solution. A stem of linear inequalities whose graphs intersect has infinite many solutions.
You can think of a function as a number generator. If you input one number into the function, the function outputs a second number. The first coordinate in each ordered pair is the input number, a member of the domain. The second coordinate in each ordered pair is an output number, a member of the range.
8-2 Equations with Two Variables
The coordinates of every point on a line in a coordinate plane make the equation of the line a true statement. Since a line has infinite length, a linear equation has an infinite number of solutions. Any equation that can be written inthe form y-mx+b is a linear function whose graph is a line. So y=3, where m=0 and b=3, is a linear function. However, the equation x=3 is not a function. It is a vertical line and therefore does not pass the vertical-line test.
8-3 Slope and y-intercept
A formula for the slope of a non-vertical line is m = (y2-y1)/(x2-x1), where m is the slope and  (x1,y1) and (x2,y2) are two points on the line. You may choose any two points on the line to calculate the slope.
8-4 Direct Variation
A direct variation is a liner function of the form y=kx, where k does not = 0. It can be expressed as “y varies directly with x”. For all solutions of y=kx, where k doesn’t = 0 and x doesn’t equal zero, the ratio y/x is always the same; it equals k, the constant of variation, which is also the slope.
8-6 Solving Systems of Linear Equations
Any two nonparallel lines on a coordinate plane intersect. The coordinates of the point of intersection form a solution of the equations for both lines.
8-7 Linear Inequalities
A system of linear equations whose graphs intersect in one point has only one solution. A stem of linear inequalities whose graphs intersect has infinite many solutions.