Mid-Chapter Quiz
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An alternative method to determining the number of solutions to a system of equations by graphing is to compare the slope and y-intercept of the equations.
y=mx+ b
| Slope | y-intercept | Graph Description | Classification |
|---|---|---|---|
| m_1 ≠ m_2 | irrelevant | intersecting lines | consistent, independent |
| m_1=m_2 | b_1≠ b_2 | parallel lines | inconsistent |
| m_1=m_2 | b_1=b_2 | same line | consistent, dependent |
Let's write the equations in the given system in slope-intercept form, highlighting the m and b values.
| Given Equation | Slope-Intercept Form | Slope m | y-intercept b |
|---|---|---|---|
| y=2x-1 | y=2x+( -1) | 2 | (0, -1) |
| y=-2x+3 | y=-2x+ 3 | -2 | (0, 3) |
Comparing the slopes, we see that they are not equal, so the lines are intersecting. This means that the system is consistent and independent.