Linear Equations
Recall:
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.
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