CONNECTIONS: SOLUTIONS AND INTERCEPTS

GOAL: To be able to use a graph to check an algebraic solution


We have been working with graphs of linear equations.

How do the graphs relate to linear equations of one variable?

Solve 2x+10=0 for x. x=-5

What does it mean that -5 is a solution to this equation?

Let's look at the graph of y=2x+10:

Notice that x=-5 is the x-intercept of this graph.

Or, the point where y=0.

In other words, the x-intercept of the line y=2x+10 is the solution of the equation 2x+10=0.


Using a Graphic Check of a Solution

The solution of a linear equation involving one variable x can be checked graphically with the following steps:

1. Write the equation in the form ax+b=0

2. Sketch the graph of y=ax+b

3. The solution of ax+b=0 is the x-intercept of y=ax+b


One Variable Equation

The solution of ax+b=0 is -(b/a)

Two Variable Equation

The x-intercept of the graph of y=ax+b is -(b/a)

Use graphing calculator to approximate the solution of:

(4/5)(3x-2)=25-(5/6)x

HINT: Rewrite the equation as (4/5)(3x-2)-[25-(5/6)x]=0.

The solution is the x-intercept of the line y=(4/5)(3x-2)-[25-(5/6)x]


EXTENSION: (Solve each equation graphically)

1. 7x-4=24

2. -3x-7=38


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