F&P Math 10 Notes

Lesson 5: Equation of a Line Using Point-Slope Form - 1 We need to be able to make an equation for a line given some information. To do this we need to remember 2 formulas:

bmxyxx

yym

12

12

Easy case: Given slope and y-intercept.

Example 1: Find the equation of a line with slope 5

3 and y-int 7 .

Harder case: Given slope and a point (not y-int.)

We will use a modified slope formula 1

1

xx

yym

and

Plug slope in for m and the point into ),( 11 yx Example 2: Find the equation of a line passing through (-2, 5), with a slope of -3.

1. sub into equation 2. cross multiply

point-slope form of the equation slope-intercept form

Math 10 FP

The Point-slope from of an equation is written as: _________________________, where (x1,y1) is a point on the line and m is the slope. Both the slope and the point can be identified from the equation!

Example 3: Find equation of line with slope 3

2 passing through (3,4),

using both slope-intercept form and point-slope form. Example 4: Write an equation in point-slope form of the line that

passes through (-2,-3) and has a slope of 4

1.

Example 5: Identify the slope of the line and a point on the line from this equation:

24

35

xy

Math 10 FP

Lesson 6: Point-Slope Form of a Linear Equation - 2 More Examples:

1) Write an equation for the line (in both point-slope and slope-intercept form) that passes through (1, -1) and is:

a) parallel to the line 53

2 xy

b) perpendicular to the line 53

2 xy

Math 10 FP

2) Write an equation for the line (in both point-slope and slope-intercept form) that passes through (2, -3) and is:

a) parallel to the line 53 xy

b) perpendicular to the line 53 xy

page 372 # 4-7ac, 9ac,10,11ac,12,14,20a,21,24