Algebra Tutorials!

 Sunday 19th of May

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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 Solve for:

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# Linear Equations

Recall:

• Graphing a line.
• What the graph means.
• Slope.
• x - and y -intercepts.

New Stuff:

• Slope-intercept form of the equation.

The graph of the equation y = mx + b is a straight line with slope m and y -intercept ( 0 ; b ).

Procedure: (Writing an Equation in Slope-Intercept Form)

To write a linear equation in slope-intercept form, solve the equation for y .

Examples:

Write the equations in slope-intercept form. Then find the slope and y-intercept.

1. 8x + 2y = -6

2. -5x + y = 15

• Using the y -intercept and the slope to draw a graph.

Procedure: (Using the y -intercept and Slope to Graph a Line)

1. Find the slope and write it as a fraction (i.e. if the slope is 2, write it as ).

2. Find the y -intercept and plot it. This is your starting point.

3. From the starting point:

• If the slope is positive, move up the distance on the top of the fraction and right the distance on the bottom of the fraction to find a second point.
• If the slope is negative, move DOWN the distance on the tope of the fraction and right the distance on the bottom of the fraction to find a second point.

4. Starting at the second point you found above, repeat the previous step to find a third point.

5. Connect the points with a straight line and extend the line straight in each direction.

Example:

Graph both of the equations in the previous example on the same set of axes.

• Solving equations graphically.

Procedure: (Solving Equations Graphically)

1. Graph each side of the equation.

2. Find all points of intersection.

3. The x coordinates of the points of intersection are the solutions.

Example:

Solve the equation -4x - 3 = 5x + 15 graphically.