how is a linear function graphed?
- construct a table of values with the independent variable as the first row and the dependent variable as the second row
- draw a number plane with the independent variable on the horizontal axis and the dependent variable as the vertical axis. plot the points
- join the points to make a straight line
what is the gradient-intercept formula?
y = mx + c
where m - slope or gradient of the line (vertical rise over the horizontal run)
c - y-intercept; where the line cuts the y-axis or vertical axis
how are a pair of simultaneous equations solved graphically?
- draw a number plane
- graph both linear equations on the number plane
- read the point of intersection of the two straight lines
- interpret the point of intersection for practical applications
how are simultaneous equations solved using the substitution method?
- make one pronumeral the subject in one of the equations
- substitute the expression for this subject into the other equation
- solve this new equation to find the value of one pronumeral
- substitute this value into one of the equations to find the value of the second pronumeral
how are simultaneous equations solved using the elimination method?
- make sure that the two coefficients of one pronumeral are the same. this may require multiplying or dividing one or both equations by a number
- eliminate one pronumeral by adding or subtracting the two equations
- solve this new equation to find the value of one pronumeral
- substitute this value into one of the equations to find the value of the second pronumeral
how do simultaneous equations work as models?
simultaneous equation models use two linear functions to describe a practical situation and the point of intersection is often the solution to a problem
how is the break-even point of a graph found?
break-even point occurs when cost equals income.
profit = income - costs
income: I = mx
costs: C = mx + c
