- Write the equation of a line in three forms.
- Identify key components of a line from a given equation.
- Express the solution to a linear inequality graphically.
- Coefficients – Numbers that multiply variables.
- The number in front of a variable
- Can be negative or positive
- Ex. 4x: coef is 4
- Ex. -x: coef is -1
- Ex. -3/5: coef is -3/5
- Coordinates – locations on a map
- In math, (x,y) are the coordinates that represent a point located on the Cartesian plane
- (x,y) are in alphabetical order, and you start plotting points with the x-axis first, then the y-axis
- Linear Inequality – An inequality in which the variable is of degree one.
- The graph of this line is shaded above or below the line
- The graph may or may not include the line itself (depends if the inequality has an equal bar under it or not)
- Point-Slope Form – The equation of a straight line in the form:
- The x and y in the equation remain part of the equation. Do not substitute a value for these.
- The represent ANY point on the line. You choose!
- Slope-Intercept Form – A form of a linear equation that includes the slope of the line and the value of they-intercept.
- Form: y = mx + b
- m: slope (the coefficient of x)
- b: y-intercept (written as (0,b))
- Standard Form of a Linear Equation – Form: Ax + By + C = 0.
- Undefined – A value that cannot be computed.
- The slope of the vertical line below is undefined (ex. x=3) because it is ALL rise and NO run.
- Zero Slope – A horizontal line has no slope, also known as a zero slope (ex. y=2) because it is NO rise and ALL run.
Answer: There is a bar, so the border line is solid. The y-coordinates are BELOW () the line, so shade below the border line.
|Linear Equations in the Real World|