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.
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
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