Code de contenu
m1567
Slug (identifiant)
linear-relationships
Niveaux
Secondary II
Secondary III
Matière
Mathematics
Tags
linear
slope
rate of change
Introduction

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.

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Things to Know Before You Start
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Corps

To follow this Crash Course, you should:

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Key Takeaways
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Corps

The rule for a linear relationship is |y = ax + b.|

  • |\boldsymbol{a}=| slope (rate of change) ||\text{Slope}(a)=\dfrac{y_2-y_1}{x_2-x_1}||

  • |\boldsymbol{b}=| initial value (y-intercept)

To find the slope (parameter a):

  1. Identify 2 points (or pairs) belonging to the line.

  2. Choose one point to be |(x_1,y_1)| and the other |(x_2,y_2).|

  3. Substitute these points into the slope formula: |\text{Slope}(a)=\dfrac{y_2-y_1}{x_2-x_1}.|

  4. Solve the resulting equation.

Things to consider when finding the slope:

  1. 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.

  2. 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}|):

  1. Calculate the rate of change using the slope formula.

  2. Write the equation, substituting this value for parameter |\boldsymbol{a}.|

  3. 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).

  4. Rewrite the equation, substituting the found values for both |\boldsymbol{a}| and |\boldsymbol{b}.|

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Largeur de l'exercice
720
Hauteur de l'exercice
720
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720
Hauteur de l'exercice
720
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For more help
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Nombre de colonnes
2 colonnes
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Concept Sheets
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Exercises
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Durée
42 minutes
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