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# Equations of lines.

## Presentation on theme: "Equations of lines."— Presentation transcript:

Equations of lines

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.

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).

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).

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}

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}

x-intercept Point where a line crosses the x-axis. (#, 0)
Find by setting y = 0 and solving for x.

y-intercept Point where a line crosses the y-axis. (0, #)
Find by setting x = 0 and solving for y.

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.

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

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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