How to Construct & Interpret a Linear Function from a Table | 8.F.B.5 | Grade 8 Math 💗
In this math video lesson we will learn how to construct and interpret a linear function from a table. We will consider a linear relationship shown in an input-output table. We will first identify a missing y value from the table that models a linear relationship. We will understand that a linear relationship has a constant rate of change. We will identify the constant rate of change between the x values and the y values. We will use this constant rate of change to complete the table and identify the missing y value. We will also identify the slope of the linear function by identify the ratio of the change in y to the change in x. We will also use the slope formula to find the slope of the linear relationship. We will identify the y-intercept of the linear function by understanding the the input or x value of zero identifies the y-intercept of the function. We will write the equation of the linear function in form y=mx+b which is slope-intercept form. We will then use the equation of the function to interpret a relationship and identify if a point lies on the line. We will understand that a point on a line is a solution of the linear equation. A four part student practice problem is modeled and explained.
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00:00 Introduction
00:10 Lesson Objectives
00:27 Essential Question
00:40 Complete the Table of a Linear Relationship
02:23 Find the Slope & y-intercept from a Table
04:08 Write an Equation of a Line from a Table
05:12 Does the Point lie on a Line?
07:03 Student Practice - 4 Parts
08:01 Identify y-intercept from a Table
08:48 Using the Slope Formula
10:24 Slope-Intercept Form
11:11 Does the Point Lie on a Line?
Functions
Use functions to model relationships between quantities.
8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.