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Equations of lines

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**Given the slope and y-intercept.**

Use slope-intercept formula. Substitute the slope for m. Substitute the y-intercept for b. Ex. Write the equation of a line that has a y-intercept of -3 and a slope of ½.

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**Given the slope and a point.**

Use point-slope formula. Substitute the slope for m. Substitute the point for (x1, y1). Ex. Write the equation of a line that has a slope of 2 and passes through the point (-1, -3).

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Given two points. Use the slope formula. Find the slope. Use point-slope formula. Substitute the slope for m. Substitute one of the given points for (x1, y1). Ex. Write the equation of a line passes through the points (0, -3) and (4, 5).

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**D: {2}, R: {all real numbers}**

Vertical Lines Have an undefined slope. Equation: x = # Domain is a single x-value. Range is all real numbers. Example x = 2 D: {2}, R: {all real numbers}

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**D: {all real numbers}, R: {2}**

Horizontal Lines Have a slope of zero. Equation: y = # Domain is all real numbers. Range is a single y-value. Example y = 2 D: {all real numbers}, R: {2}

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**x-intercept Point where a line crosses the x-axis. (#, 0)**

Find by setting y = 0 and solving for x.

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**y-intercept Point where a line crosses the y-axis. (0, #)**

Find by setting x = 0 and solving for y.

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**The graph has a slope of -3 and a y-intercept of 4.**

Describing a graph Describe a graph of a linear equation using the slope and y-intercept. First write the equation in slope-intercept form. Ex. 3x + y = 4 y = -3x + 4 The graph has a slope of -3 and a y-intercept of 4.

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**Parallel Lines Ex. y = -3x + 4 and y = -3x – 3 Same slope**

Different y-intercepts Parallel lines will NEVER intersect. Ex. y = -3x + 4 and y = -3x – 3

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**Perpendicular Lines Ex. y = -3x + 4 and y = (1/3)x – 3**

Slopes are opposite reciprocals Different y-intercepts Perpendicular lines form 90 degree angles at their intersection. Ex. y = -3x + 4 and y = (1/3)x – 3

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