6.3 Solving linear equations by graphing

From a previous chapter on linear relations, we learned that Linear Relations are basically relationships that show a graph with a straight line traversing the x axis and the y axis diagonally. This relationship illustrates that as the value of x increases or decreases, the value of y increases or decreases too. We also learned that if you are not seeing a straight line in your grid paper, then it means it’s not a linear relationship.

In the chapter on linear equations, we learned all about linear equations and their table of value. In this chapter however, instead of just looking at a certain graph that’s made from a table of values, we would be learning how to represent patterns into a linear relation. In 6.1 we have activities that would use shapes and other figures to illustrate linear relation.

In 6.2, not only do we rely into looking at the table of values to know the value of a certain variable but also we would learn how to look at the graph so we could solve for the value of a particular variable. This is done by using the graph to deduce the equation. The equation is consisted of variables, numerical coefficient, and the constant. So if we have y = 3x + 4, 3 is the numerical coefficient, x and y are the variables and 4 is the constant. There are series of values in just a single line graph and not all of these are listed in the table of values so with 6.2 we would be able to strengthen our ability to read graphs. To check your graph and the values of your x and y, you can go to an online graphing calculator.

Finally, in 6.3 we will learn how to solve word problems by graphing the equation given. From our previous discussion on linear equations, we know that the general formula is y = mx + b where m is the slope, and b is the y intercept. We are to use that to interpolate the values that would be found in the line and to extrapolate on the trend if ever needed in order to solve the problem.

Solving linear equations by graphing

We will learn how to plot linear equations, and then use the graphs as an aid to answer questions about the linear relations. Alternatively, we can find out the linear equations from their graphs. In addition, we will learn how to plot graphs and determine their equations when we are given the table of values of linear relations. We will also explore the concepts of interpolating and extrapolating data from graphs of linear equations.

Lessons

  • 1.
    A train travels at a speed of 120km/h. The equation that represents the relationship of distance (d) and time (t) is d=120t.
  • 2.
    The graph shows the relationship of the temperature of water, c, and time, t, as the water boils.

  • 3.
    Plot the graph for each set of values. Then, find the equation that represents each relationship.
  • 4.
    Mark ran a marathon. Below is the record of how he did.

    Time, t (h)

    Distance, d (km)

    0.5

    4.2

    0.8

    6.7

    1.3

    10.9

    2.9

    24.4

    3.5

    29.4

    4.2

    35.3

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Solving linear equations by graphing

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