Graphing Equations

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Graphing Equations

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Graphing Equations- use slope and y -intercept of a line
1. Calculating slope- Rise over run (Change in y/Change in x)
2. slope-intercept form (y= mx + b)
  1. Find slope (m)
  2. Find y- intercept (b) Where the line crosses y axis.
3. Graphing linear equations
  1. equations between two variables that makes a straight line when plotted on a graph.
    1. Can use slope-intercept form (y=mx + b) to graph
    2. Can use sample points (x,y)
4. Graphing linear inequalities
  1. A linear inequality contains one of the symbols of < or >It shows the data which is not equal in graph form.

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Welcome to this lesson on Graphing equations. Today we are going to look at the basics of what is needed to graph and interpret graph values.

So this quote by Charlie Munger, an American investor I thought was a good explanation as to what graphs are ultimately for…. to help us understand what numbers mean.

So often times when we look to collect data we can see if there are trends or correlations that can be inferred. Graphs assist us in understanding what number values mean. For a linear equation, we use both slope and y-intercept. The slope is can be calculated by measuring the change in Y and dividing it by the change in x. The variable for slope is m. Where the line crosses the y-axis is the y-intercept (represented as a(b). And the slope-intercept form is y=mx+b

Linear equations with two variables may appear in the form Ax + By = C, and the resulting graph is always a straight line. But more often, the equation takes the form y = mx + b, where m is the slope of the line of the corresponding graph and b is its y-intercept, the point at which the line meets the y-axis. So here is a sample linear equation 2y= -4x+8. Let’s convert that to the slope-intercept form and now we can identify the y-intercept and plot it. We can also determine the slope of the line and thus draw a line through the y-intercept with the correct slope. and lastly, we can verify the graph by taking a number value on the line and plugging it into the equation to see if the coordinate values match up.

Another graph in algebra is done to show linear inequalities and it will contain greater than or less than symbols. It shows the data which is not equal in graph form. We can approach this in a similar fashion in that we want to put it in slope-intercept form and graph the line, but this time using a dotted line if < or >. You will then shade above the line if the inequality is greater than and shade under the line if the inequality is less than.

So in this image on the left we have a line graph showing where the line is created as equality, then because it is a less than sign you shade in below the line (that should be dotted representing the area not included or unequal to the values of the equation.

In review, the slope is an important value of a line that shows the change in y over change in x. The y-intercept is symbolized as b and determines where the line crosses the y axis. linear equations show relationships between two variables and can be graphed and linear inequalities show data which is not equal in graph form.

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