In this set of Math Tutorials we cover Linear Graphs in detail with clear guides, Linear Graphs formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Linear Graphs calculators.
We also provide online Linear Graphs Calculators which allow you to calculate specific Linear Graphs formula in support of the tutorials or to check and verify your own calculations in support of your Linear Graphs homework, math coursework or to help you improve your own understanding so it is easier to teach your children Linear Graphs.
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This chapter deals with linear graphs since they are very widespread in algebra and mathematical analysis. The first tutorial provides an overview of linear graphs, where the most basic properties of such graphs are reviewed, given that linear equations, functions and their graphs are not discussed for the first time here. This tutorial deals with the elements of linear graphs and with certain special linear graphs such as horizontal and vertical ones. A new item explained in this tutorial is how to find the distance between two parallel horizontal or vertical graphs. Then, it follows with steeped graphs and their features. In the end, the domain and range of linear graphs are explained, where you can learn the procedure used to plot a linear graph with a limited domain.
The second tutorial deals with slopes and gradients. It begins with the mathematical definition of slope and gradient and the difference between these two close terms. The gradient's formula is provided with illustrated examples. The tutorial concludes with the sign of the gradient and its meaning, including the special cases when the graph is purely horizontal or vertical.
The third tutorial focuses on the equation of linear graphs. It begins with a revision of linear equations including the elements (variables, coefficients and constants) involved in them. Then, the tutorial continues with the two methods used for expressing linear equations (general and simplified). Another important item discussed in this math tutorial is finding the intercepts of a linear graph with horizontal and vertical axes. The concept of the gradient is discussed again in this tutorial from a new perspective, where the focus is to know how to write the equation of a linear equation or function using the gradient. Finally, you will learn how to find the equation of a line with two known points and how to find the equation of a line from a given graph.
The fourth tutorial highlights the three possible mutual combinations of two linear graphs: parallel, perpendicular and intersecting, including the conditions to obtain each of these combinations. More precisely, you will discover the condition two lines must have to be parallel, perpendicular and/or intersecting. Next, you will learn what it means for two lines with the same coefficient and constant. Another question addressed in this tutorial is: how to find the equation of a line that is parallel to another known line and what other must we know for this? The focus then shifts to perpendicular graphs, where we explain key points like: what is the relationship between gradients in perpendicular lines; how to find the equation of a line that is perpendicular to another known line; How to find the intercept of two perpendicular lines; and so on. The tutorial continues with the intersecting lines, where items like the conditions for two lines to be intersecting, finding the common point, etc. We conclude the tutorial by explaining how to find the distance between two parallel lines.
The fifth and last tutorial of this chapter focuses on line segments, where concepts like interval, segment, half-interval and half-segment are explained, illustrating them with examples. The tutorial begins with the definition of interval and segment; then it follows with the meaning of half-interval and half-segment. Another question addressed here is how to show intervals and segments in a number line. The tutorial follows with the definition of a line segment, also highlighting its importance. The tutorial and chapter conclude by discussing items like: how to find the midpoint of a line segment; how to find the length of a line segment; How to find the missing coordinates of a point on a line segment if the ratios are known; and so on.
The following Math Calculators are provided in support of the Linear Graphs tutorials.