Writing Simple Linear Equations

Learn slope-intercept models, using a point to find an intercept.

Lesson 2 of 32 parts Practice Flashcards

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Slope-Intercept Models

Objective: Explain slope-intercept models, apply the stated method, and check its conditions.

A line with slope m and y-intercept b has equation y=mx+b. Substitute a known input to predict an output. Context can restrict the domain to nonnegative or integer inputs; an algebraic prediction outside that domain may not be meaningful. Use only contextually allowed inputs.

Formulas

$y=mx+b$

Worked examples

Try itA linear rule has slope 6 and passes through (0,7). What output does it predict at x=7?Show answer

Step 1: The intercept is 7, so y=6x+7. Step 2: Substitute x=7. Step 3: y=49.

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Slope-Intercept Models

Objective: Explain slope-intercept models, apply the stated method, and check its conditions.

Formulas

$y=mx+b$

Worked examples

Try itA linear rule has slope 6 and passes through (0,7). What output does it predict at x=7?Show answer

Step 1: The intercept is 7, so y=6x+7. Step 2: Substitute x=7. Step 3: y=49.

Using a Point to Find an Intercept

Objective: Explain using a point to find an intercept, apply the stated method, and check its conditions.

If slope m and a point (x₀,y₀) are known, b=y₀−mx₀. This identifies the unique line with that slope through the point. Verify the completed equation by substituting the original point and checking the stated slope. A point’s y-coordinate is the intercept only when its x-coordinate is zero.

Formulas

$b=y₀−mx₀$

Worked examples

Try itA line has slope 6 and passes through (7,49). Find its y-intercept.Show answer

Step 1: Use y=mx+d with m=6. Step 2: 49=6(7)+d. Step 3: d=7.

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