Download EQUATIONS OF LINES

EQUATIONS OF LINES
Slope-intercept form; y=mx+b
Point-slope form; y 2 –y 1 =m(x 2 –x 1 )
Standard Form: Ax+By=C
Review of Point-Slope Form: Given a slope and any point (x1,y1) è
Given a slope = 2; and a point (-3, 6)
Write an equation of a line in point-slope form.
y2–y1=m(x2–x1)
y–yk=m(x–xk)
Now convert it to slope-intercept form: (y=mx+b)
Exercises: Please do on a separate sheet of paper.
1. Write an equation in Point-Slope form, and then convert it to Slope-intercept
form given a slope = -4, and the line passes thru (6,-5).
2. Write an equation in Point-Slope form, and then convert it to Slope-intercept
form: given the line passes thru the points (-2,-3) and (4,1).
STANDARD FORM:
Ax+By=C
è
2x+3y=12
Rules:
1) Variables x and y must be together on left side of = sign.
Constants on right side of = sign.
Marylynn Sciretta
2)
Variable X must be first and it must be positive.
3)
Coefficients must be integers (Wipeout fractions).
Wednesday, January 23, 2013 3:13:10 PM Eastern Standard Time
Example 1:
Rule #1)
y = 2x + 12
Rule #2)
Rule #3)
Example 2:
Rule #1)
y=
2
1
x−2
3
3
Rule #2)
Rule #3)
Exercises: Please continue to do on the separate sheet of paper.
Convert the following equations into Standard Form.
Marylynn Sciretta
1.
y = -11x – 4
2.
x – 8y + 2 = 0
3.
y = -2/3x – 1
4.
3y - 2x = 6
Wednesday, January 23, 2013 3:13:10 PM Eastern Standard Time
Example 3:
Given a slope = -2;
and a point (3,7)
Write an equation of a line in standard form.
You must begin by using point-slope form.
Rule #1)
Rule #2)
Rule #3)
Example 4:
Given a slope = ½;
Write an equation of a line in standard form.
You must begin by using point-slope form.
Rule #!)
Rule #2)
Rule #3)
Marylynn Sciretta
Wednesday, January 23, 2013 3:13:10 PM Eastern Standard Time
and a point (4,-5)
Example 5:
Write
1)
2)
3)
Given a slope = 1/6;
and a point (-2,4)
an equation of a line in:
point-slope form;
slope-intercept form; and
standard form.
You must begin by using point-slope form.
Slope intercept form
Example 6:
Write
4)
5)
6)
Standard form
Given two points: (4,5) (6,9)
an equation of a line in:
point-slope form;
slope-intercept form; and
standard form.
You must begin by using point-slope form.
Slope intercept form
Marylynn Sciretta
Wednesday, January 23, 2013 3:13:10 PM Eastern Standard Time
Standard form
Example 7:
Write
7)
8)
9)
Given two points (-2,8) (2,-8)
an equation of a line in:
point-slope form;
slope-intercept form; and
standard form.
You must begin by using point-slope form.
Slope intercept form
Marylynn Sciretta
Wednesday, January 23, 2013 3:13:10 PM Eastern Standard Time
Standard form
Exercises: Continue to do on the separate sheet of paper.
1)
Given m=4; and the point (1,5)
Write
1)
2)
3)
an equation of a line in:
point-slope form;
slope-intercept form; and
standard form.
You must begin by using point-slope form.
2)
Write
1)
2)
3)
Given m=1/4; and the point (-8,-2)
an equation of a line in:
point-slope form;
slope-intercept form; and
standard form.
How do you begin?
3)
Given two points (-2,3) and (2,5)
Write an equation of a line in:
1) point-slope form;
2) slope-intercept form; and
3) standard form.
How do you begin?
4)
Given two points (-2,-5) and (-7,-6)
Remember to convert mixed numbers to improper fractions
before “wipeout”
Write an equation of a line in:
1) point-slope form;
2) slope-intercept form; and
3) standard form.
How do you begin?
Careful with the fractions!!
Thank you, and please have the assignment ready for the next class.
Marylynn Sciretta
Wednesday, January 23, 2013 3:13:10 PM Eastern Standard Time