This Crash Course focuses on linear relationships and their possible representations. You can use the interactive videos, recap and practice questions to review this topic.
To follow this Crash Course, you should:
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know how to read a table of values
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know how to read points on a Cartesian plane
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understand operations with integers
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know how to solve equations (how to isolate a variable)
The rule for a linear relationship is |y = ax + b.|
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|\boldsymbol{a}=| slope (rate of change) ||\text{Slope}(a)=\dfrac{y_2-y_1}{x_2-x_1}||
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|\boldsymbol{b}=| initial value (y-intercept)
To find the slope (parameter a):
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Identify 2 points (or pairs) belonging to the line.
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Choose one point to be |(x_1,y_1)| and the other |(x_2,y_2).|
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Substitute these points into the slope formula: |\text{Slope}(a)=\dfrac{y_2-y_1}{x_2-x_1}.|
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Solve the resulting equation.
Things to consider when finding the slope:
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Be careful when there is a double negative. Note that there is a minus sign in the equation, and a negative sign on the number. Subtracting a negative number is equivalent to adding a positive number.
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Be sure to place the y-coordinates in the numerator, and the x-coordinates in the denominator. The equation for slope is |\text{Slope} = \dfrac{y_2-y_1}{x_2-x_1}| and not |\text{Slope} =\dfrac{x_2-x_1}{y_2-y_1}.|
To find the equation of the line (parameters |\boldsymbol{a}| & |\boldsymbol{b}|):
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Calculate the rate of change using the slope formula.
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Write the equation, substituting this value for parameter |\boldsymbol{a}.|
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Substitute a known point into this equation for |x| and |y| and solve for parameter |\boldsymbol{b},| or identify it from the graph (if possible).
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Rewrite the equation, substituting the found values for both |\boldsymbol{a}| and |\boldsymbol{b}.|