Texas Instruments TI-83 Plus Manual Book page 99

Chapter 3: Linear Functions
Linear Functions: Slope-Intercept Form
Objectives
To review the form of the equation y = mx + b, where m is slope and b is the y-intercept.
To view graphing lines and developing equations from data.
To view tables of values and graphing lines from an equation of the form y = mx + b.
To emphasize three ways of looking at lines, tables, graphs and equations.
To develop the equation of a line from information given, such as slope and y-intercept, point
and slope, and two points.
To review the slope of parallel and perpendicular lines.
Math Highlights
This section highlights a review of the slope-intercept form of a line, y = mx + b. Students will
review graphing a line using one point and the slope of the line. They will also see the equation of
a line developed inductively from data by simulating the amount of volts produced by lining up
batteries in series. Students will also review how to find a table and graph a line using the
equation y = mx + b.
A review of calculations follow, which show the step-by-step procedures needed to find the
equation of a line given, the slope and y-intercept, the slope and a point on the line, and finally
two points.
Common Student Errors
When students perform the calculations to find the equation of a line given the slope and
y-intercept, the slope and a point on the line, or two points, they often have problems
following the steps. For example, given two points, the student needs to perform three steps.
First, the student needs to calculate the slope of the line. Students may forget the formula for
slope, and then be careless about substituting the correct values in the formula. Also, they
may make errors in sign. In the second step, they need to find b using the calculated slope
and one of the points. Students need to understand that they could pick either point for this
calculation. If the slope is incorrect from the first step, the error cascades into the rest of the
solution. In the third step, they need to place all of the information into the final answer as
y = mx + b.
Students become comfortable using the variables x and y. They should be exposed to the use
of other letters for the independent and dependent variables. Students should be able to
recognize, for example, D = 2T + 4 as a linear relationship with independent variable T,
dependent variable D, a slope of 2 and the D-intercept as 4. They need to learn that they will
need to change the variables so the function reads y = 2x + 4 in order to graph it on the
calculator.
Topics in Algebra 1 © 2001 Texas Instruments
Section 4: Slope-Intercept Form
Teacher Notes
Teacher Notes 3-33