warm-up
DESCRIPTION
Warm-up. You are driving on a road trip and you want to find out how many hours total it will take you to get to California. After driving for 4 hours, you were 280 miles from home. You are now 520 miles from home and have driven for 8 hours. How long will it take you to drive 3000 miles?. - PowerPoint PPT PresentationTRANSCRIPT
Warm-up
You are driving on a road trip and you want to find out how many hours total it will take you to get to California. After driving for 4 hours, you were 280 miles from home. You are now 520 miles from home and have driven for 8 hours. How long will it take you to drive 3000 miles?
Writing Equations of
Lines
3 Forms
Slope-InterceptPoint-SlopeStandard
**Always have the variables x & y**
Break into groups of 4.
Slope Intercept
y mx b m is the slope of the line
b is the y-intercept of the line
Example
1) Write the equation of the line that has a slope of 4, and a y-intercept of -2.
2) Write the equation of the line between the points (2, 4) and (4, 12).
Example
3) Write the equation of the line pictured.
Point-Slope
1 1( )y y m x x
(x1, y1) is a point on the line
m is the slope of the line
Examples
4) Write the equation of the line that passes through the point (4, -2) and has a slope of 6.
5) Write the equation of the line that passes through the points (1, 8) and (-2, 6).
Standard Form
Ax By C Where A, B & C are integers
A is NOT negative
Putting Equations into Standard Form
1) Put the equation into slope-intercept form.
2) Subtract mx from both sides (EX: y = 3x + 7 becomes –3x + y = 7)
3) If the number in front of x is negative, multiply everything by -1.
4) If the number in front of x is a fraction, multiply everything by the denominator.
Examples6) Write the equation of the line that
passes through the points (2, 6) and (3, -3) in standard form.
7) Write the equation of the line that has slope -5 and passes through the point (1, -4) in standard form.
8) Write the equation of the line through the points (3, -5) and (7, 1) in standard form.
Pop Quiz• You are given the slope of a line and a
point on the line. How can you find an equation of the line?
• You are given the slope of a line and the y-intercept of the line, how can you find an equation of the line?
• You are given the x-intercept and the y-intercept of a line, how can you find an equation of the line?
WRITE THIS
1) Given slope (m) and y int (b): plug into y = mx + b
2) Given slope (m) and a point (x, y): plug into y = mx + b to find b. Then go to step 1.
3) Given two points (x1,y1) and (x2, y2): First find slope, then go to step 2.
Exit Ticket
9) Write the equation of the line perpendicular to the line y = ½ x + 8 through the point (1, -7) in all 3 forms.
Flipped
Slope Intercept
y mx b m is the slope of the line
b is the y-intercept of the line
Example
1) Write the equation of the line that has a slope of 4, and a y-intercept of -2.
2) Write the equation of the line between the points (2, 4) and (4, 12).
Example
3) Write the equation of the line pictured.
Point-Slope
1 1( )y y m x x
(x1, y1) is a point on the line
m is the slope of the line
Examples
4) Write the equation of the line that passes through the point (4, -2) and has a slope of 6.
5) Write the equation of the line that passes through the points (1, 8) and (-2, 6).
Standard Form
Ax By C Where A, B & C are integers
A is NOT negative
Putting Equations into Standard Form
1) Put the equation into slope-intercept form.
2) Subtract mx from both sides (EX: y = 3x + 7 becomes –3x + y = 7)
3) If the number in front of x is negative, multiply everything by -1.
4) If the number in front of x is a fraction, multiply everything by the denominator.
Examples6) Write the equation of the line that
passes through the points (2, 6) and (3, -3) in standard form.
7) Write the equation of the line that has slope -5 and passes through the point (1, -4) in standard form.
8) Write the equation of the line through the points (3, -5) and (7, 1) in standard form.
Pop Quiz• You are given the slope of a line and a
point on the line. How can you find an equation of the line?
• You are given the slope of a line and the y-intercept of the line, how can you find an equation of the line?
• You are given the x-intercept and the y-intercept of a line, how can you find an equation of the line?