1.given slope (m) and y-intercept (b) create the equation in slope- intercept form. 2. look at a...
TRANSCRIPT
Chapter 5 Reivew
1.Given slope (m) and y-intercept (b) create the equation in slope-intercept form.
2. Look at a graph and write an equation of a line in slope-intercept form.
3. Know how to plug into point-slope form.4. Find the slope between two points.5. Write an equation of a line that passes through two points.6. Find an equation of a line that is parallel to an equation given and
also given a random point.7. Find an equation of a line given a slope and a random point.8. Decide which two lines are parallel.9. Convert an equation into standard form.10. Write an equation of a horizontal (y = #) or vertical line (x = #).11. Decide which two lines are perpendicular.12. Look at an equation of a line and find the slope of that line.
Test Topics
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y − y1 = m(x − x1)
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m =y2 − y1
x2 − x1
Various Forms of an Equation of a Line.
Slope-Intercept Form
Standard Form
Point-Slope Form
slope of the line
intercept
y mx b
m
b y
, , and are integers
0, must be postive
Ax By C
A B C
A A
1 1
1 1
slope of the line
, is any point
y y m x x
m
x y
Review 5.1-5.2
Let’s try one…
Given “m” (the slope remember!) = 2And “b” (the y-intercept) = +9
All you have to do is plug those values intoy = mx + b
The equation becomes…y = 2x + 9
Write the equation of a line after you are given the slope and y-intercept…
Given m = 2/3, b = -12,Write the equation of a line in slope-intercept
form.Y = mx + b
Y = 2/3x – 12*************************
One last example…Given m = -5, b = -1
Write the equation of a line in slope-intercept form.
Y = mx + bY = -5x - 1
Let’s do a couple more to make sure you are expert at this.
GUIDED PRACTICE for Example 1
Write an equation of the line that has the given slope and y-intercept.
1. m = 3, b = 1
y = x + 13
ANSWER
2. m = –2 , b = –4
y = –2x – 4
ANSWER
3. m = – , b =34
72
y = – x +34
72
ANSWER
1) m = 3, b = -14
2) m = -½, b = 4
3) m = -3, b = -7
4) m = 1/2 , b = 0
5) m = 2, b = 4
6) m = 0, b = -3
Given the slope and y-intercept, write the equation of a line in slope-intercept form.
y = 3x - 14
y =-½x + 4
y =-3x - 7
y = ½x
y =2x + 4
y = - 3
Write an equation given the slope and y-intercept
Write an equation of the line shown in slope-intercept form.
m = ¾
b = (0,-2)
y = ¾x - 2
3) The slope of this line is 3/2?
True
False
5) Which is the slope of the line through (-2, 3) and (4, -5)?
a) -4/3b) -3/4c) 4/3d) -1/3
8) Which is the equation of a line whose slope is undefined?
a) x = -5b) y = 7c) x = yd) x + y = 0
Review 5.3-5.4Point-Slope FormStandard Form
Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2.
y – y1 = m(x – x1)
y – 1 = -2(x – 4)Substitute 4 for x1, 1 for y1 and -2 for m.
Write in slope-intercept form.y – 1 = -2x + 8 Add 1 to both sides
y = -2x + 9
Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7.
y – y1 = m(x – x1)
y – 3 = 7[x – (-1)]y – 3 = 7(x + 1)
Write in slope-intercept formy – 3 = 7x + 7y = 7x + 10
Write the equation of a line in slope-intercept form that passes through points (3, -4) and (-1, 4).
y2 – y1m =x2 – x1
4--4 =
-1-3 8 –4= = –2
y2 – y1 = m(x – x1) Use point-slope form.
y + 4 = – 2(x – 3) Substitute for m, x1, and y1.
y + 4 = – 2x + 6 Distributive property
Write in slope-intercept form.y = – 2x + 2
1) (-1, -6) and (2, 6)
2) (0, 5) and (3, 1)
3) (3, 5) and (6, 6)
4) (0, -7) and (4, 25)
5) (-1, 1) and (3, -3)
Write the equation of the line in slope-intercept form that passes through each pair of points.
GUIDED PRACTICE for Examples 2 and 3
GUIDED PRACTICE
4. Write an equation of the line that passes through (–1, 6) and has a slope of 4.
y = 4x + 10
5. Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1.
y = 3x – 14ANSWER
ANSWER
Write an equation of the line that passes through (5, –2) and (2, 10) in slope intercept form
SOLUTION The line passes through (x1, y1) = (5,–2) and (x2, y2) = (2, 10). Find its slope.
y2 – y1m =x2 – x1
10 – (–2) =
2 – 5 12 –3= = –4
y2 – y1 = m(x – x1) Use point-slope form.
y – 10 = – 4(x – 2) Substitute for m, x1, and y1.
y – 10 = – 4x + 8 Distributive property
Write in slope-intercept form.y = – 4x + 18
1) Which of the following equations passes through the points (2, 1) and (5, -2)?
a. y = 3/7x + 5 b. y = -x + 3c. y = -x + 2 d. y = -1/3x + 3
a) y = -3x – 3b) y = -3x + 17c) y = -3x + 11d) y = -3x + 5
9) Which is the equation of a line that passes through (2, 5) and has slope -3?
Write equation of the line in standard form that passes through (-1,5) and (1,9)
y2 – y1m =x2 – x1
9 – 5 =
1 – -1
4 2= = 2
y – 9 = 2(x – 1)
y – 9 = 2x - 2
y = 2x + 7
-2x + y = 7
-2x -2x
2x - y = -7
Write equation of the line in standard form that has a slope of ½ and passes through (4,-5).
y + 5 = ½(x – 4)
y + 5 = ½x - 2
y = ½x - 7
-x + 2y = -14
-x -x
x - 2y = 14
2y = x - 14
Multiply everything by 2 to get rid of the fraction
Write equation of the line in standard form that is parallel to y=⅔x-8 and passes through (6,4)
y – 4 = ⅔(x – 6)
y – 4 = ⅔x - 4
y = ⅔x
-2x + 3y = 0
-2x -2x
2x - 3y = 0
m = ⅔
3y = 2x Multiply everything by 3 to get rid of the fraction
EXAMPLE 2Write an equation in standard form of the line that passes through (5, 4) and has a slope of –3.
y – y1 = m(x – x1) Use point-slope form.
y – 4 = –3(x – 5) Substitute for m, x1, and y1.
y – 4 = –3x + 15 Distributive property
SOLUTION
y = –3x + 19 Write in slope-intercept form.
3x + y = 19
+3x +3x
Review 5.6Parallel vs. Perpendicular Lines
EXAMPLE 3
b. A line perpendicular to a line with slope m1 = –4 has a slope of m2 = – = . Use point-slope form with
(x1, y1) = (–2, 3)
14
1m1
y – y1 = m2(x – x1) Use point-slope form.
y – 3 = (x – (–2))14
Substitute for m2, x1, and y1.
y – 3 = (x +2)14 Simplify.
y – 3 = x +14
12
Distributive property
Write in slope-intercept form.
Write equations of parallel or perpendicular lines
1 7
4 2y x
y = 3 (or any number)Lines that are horizontal have a slope of zero.
They have “run” but no “rise”. The rise/run formula for slope always equals zero since rise
= o.y = mx + by = 0x + 3
y = 3This equation also describes what is happening
to the y-coordinates on the line. In this case, they are always 3.
Horizontal Lines
x = -2Lines that are vertical have no slope
(it does not exist).They have “rise”, but no “run”. The rise/run
formula for slope always has a zero denominator and is undefined.
These lines are described by what is happening to their x-coordinates. In this example, the x-
coordinates are always equal to -2.
Vertical Lines
8) Which is the equation of a line whose slope is undefined?
a) x = -5b) y = 7c) x = yd) x + y = 0
10) Which of these equations represents a line parallel to the line
2x + y = 6?
a) Y = 2x + 3b) Y – 2x = 4c) 2x – y = 8d) Y = -2x + 1