Equations of Lines Lesson 2.2

Point Slope Form We seek the equation, given point and slope (x2, y2) • m We seek the equation, given point and slope Recall equation for calculating slope, given two points Now multiply both sides by (x1 – x2) Let any point (x,y) on the line be one of the points in the equation

Point Slope Form Alternative form Try it out … For a line through point (6, -2) and slope m = -3/4 determine the equation. Show both forms (6, -2) •

Slope Intercept Form Recall that we have used y = m * x + b The b is the y-intercept Where on the y-axis, the line intersects m is the slope Given slope Observe y-intercept

Converting Between Forms What does it take to convert from point slope form to slope-intercept form? Multiply through the (x – x1) by m Simplify the expression Try it Note that this also determines the value for the y-intercept, b

Two Point Form Given (3, -4) and (-2, 12), determine the equation Find slope Use one of the points in the point-slope form

Set the style of one of the equations to Thick Parallel Lines Given the two equations y = 2x – 5 y = 2x + 7 Graph both equations How are they the same? How are they different? Set the style of one of the equations to Thick

Parallel Lines Different: where they cross the y-axis Same: The slope Note: they are parallel Parallel lines have the same slope y=2x+7 y=2x-5 Lines with the same slope are parallel

Perpendicular Lines Now consider Graph the lines How are they different How are they the same?

Perpendicular Lines Same: y-intercept is the same Different: slope is different Reset zoom for square Note lines are perpendicular

Perpendicular Lines Lines with slopes which are negative reciprocals are perpendicular Perpendicular lines have slopes which are negative reciprocals

Horizontal Lines Try graphing y = 3 What is the slope? How is the line slanted? Horizontal lines have slope of zero y = 0x + 3

Vertical Lines Have the form x = k What happens when we try to graph such a line on the calculator? Think about We say “no slope” or “undefined slope” • k

Direct Variation The variable y is directly proportional to x when: y = k * x (k is some constant value) Alternatively As x gets larger, y must also get larger keeps the resulting k the same

Direct Variation Example: The harder you hit the baseball The farther it travels Distance hit is directly proportional to the force of the hit

Direct Variation Suppose the constant of proportionality is 4 Then y = 4 * x What does the graph of this function look like? Note: This is a linear function The constant of proportionality is the slope The y-intercept is zero

Assignment Lesson 2.2A Page 86 Exercises 1 – 41 odd Lesson 2.2B