Post on 31-Dec-2015
description
Slope – Intercept Form
To write an equation of a line in slope-intercept form, you need …
… the y-intercept
… The Slope
b
m
Once you have these two things, you can write the equation as
y = m x + b
DONE
y = -2 x + 5
Write the equation of the line that slope -2 and y-intercept 5.
Example #1
y = m x + bStarting with the slope –intercept form
Plug in the slope, and the y –intercept to get
DONE
y – y1 = m (x – x1)
… The Slope …
… Any Point On The Line
Point – Slope FormTo write an equation of a line in point – slope form, all you need is …
(x1, y1)
m
Once you have these two things, you can write the equation as
DONE
Example #1Write the equation of the line that goes through the point (2, –3) and has a slope of 4.
Point = (2, –3)
Slope = 4
y – y1 = m (x – x1)
y + 3 = 4 (x – 2)
Starting with the point – slope form
Plug in the y-value, the slope, and the x-value to get
Notice, that when you subtracted the “–3” it became “+3”.
DONE
y – 6 = (x + 4)32
y – y1 = m (x – x1)
Example #2
Starting with the point – slope form
Plug in the y-value, the slope, and the x-value to get
Notice, that when you subtracted the “–4” it became “+4”.
Point = (–4, 6)
Slope = 32
DONE
32
Write the equation of the line that goes through the point (–4, 6) and has a slope of .
To use point – slope form, we need a point and a slope. Since we have two points, just pick one … IT DOESN’T MATTER … BOTH answers are acceptable… let’s see why:
We have two points, but we’re missing the slope. Using the formula for slope, we can find the slope to be
Write the equation of the line that goes through the points (6, –4) and (2, 8) .
Example #3
Point = (6, –4)
Slope = –3
y + 4 = –3 (x – 6)
Point = (2, 8)
Slope = –3
y – 8 = –3 (x – 2)
Using the first point, we have, Using the second point, we have,
DONE
34
12
x
ym
Writing Equations in Slope – Intercept Form
y + 4 = –3 (x – 6) y – 8 = –3 (x – 2)
Distribute Distribute
y + 4= –3x + 18 y – 8 = –3x + 6
Subtract 4 and combine like terms
Add 8 and combine like terms
y = –3x + 18 – 4
y = –3x + 14
y = –3x + 6 + 8
y = –3x + 14
Notice … They’re the same!
DONE
Horizontal Line: y = c , where c is a constant. Example: y = 3
Other Forms of Linear Equations
DONE
1 2 43
5
-1-2-3-4-5
1
2
3
4
5-1
-2-3
-4
-5
Vertical Line: x = c , where c is a constant. Example: x = 2
Other Forms of Linear Equations
DONE
1 2 43
5
-1-2-3-4-5
1
2
3
4
5-1
-2-3
-4
-5
Your turn:Write the equation of the line described in slope-intercept form
1.Has slope -5 and y-intercept 3
2.That contains the point (6, 2) and has slope
3.That contains (-2, -4) and has slope
4.That contains the points (4, 5) and (6, 12)
5.That contains the points (-1, 2) and (5, -4)
6.That is vertical and contains (3, 8)
7.That is horizontal and contains (2, -7)
23
DONE
8
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