algebra 3 lesson 1.3 objectives: ssbat write the equation of a line given the slope and y-intercept....
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Algebra 3
Lesson 1.3
Objectives:
SSBAT write the equation of a line given the slope and y-intercept.
SSBAT write the equation of a line given the slope and a point on the line.
SSBAT write the equation of a line given 2 points.
Standards: M11.D.3.2.2
Warm-Up 1.3
Solve each for y.
13x + 5y = 7x – 2y + 14
y = - x + 2
Writing an Equation given the Slope and Y-intercept
Substitute the slope and y-intercept into the equation y = mx + b for m and b
Write the equation of each line with the given slope and y-intercept. (y = mx + b)
1. Slope is and y-intercept is 11
m b
y = x + 11
2. Slope is -9 and y-intercept is -4
m b
y = -9x – 4
3. Slope is 0 and y-intercept is 12
m b
y = 0x + 12
y = 12
Point-Slope Form of an Equation of a Line
Used to write the equation of a line given
1) A point on the line and the slope2) 2 points on the line
y - y1 = m(x - x1)
Where m is the slope and (x1 , y1) is a point on the line.
Writing the equation given the slope and a point on the line
1. Substitute the slope in for m and the point in for x1 and y1 into y – y1 = m(x – x1)
2. Put the equation in the correct form (slope-intercept or standard form given in directions)
Examples: Write an equation with the given point and slope.Write your answer in slope-intercept form.
1. Slope is 5 and through (4, -2)
m x1 y1
y – -2 = 5(x – 4)
y + 2 = 5x – 20
y = 5x – 22
y – y1 = m(x – x1)
2. Slope is ½ and through (-8, 1) m x1 y1
y – 1 = ½(x - -8)
y – 1 = ½ (x + 8)
y – 1 = ½ x + 4
y = ½ x + 5
3. Slope is and through (-1, 5)
5
2
y – 5 = (x - -1)
y – 5 = (x + 1)
5
2
5
2
0.4 5
2 5 xy
.4 5 5
2 xy
4. Slope is and through (0, 7)
4
3
y – 7 = (x – 0)
4
3
0 4
3- 7 xy
7 4
3 - xy
Writing the equation of a line given 2 points
1. Find the slope between the 2 points
m =
2. Use the slope from above and choose 1 of the given points to substitute into the point-slope equation: y – y1 = m(x – x1)
1. (8 , -1) and (2 , 5)
82
)1(5
m 6
6
1-
)8(1)1( xy
y - y1 = m(x - x1)
811 xy
71 xy
Write the equation of the line that goes through the 2 points. Write your answer in slope-intercept form.
2. Through (4, -1) and (1, 5)
41
15
m
Choose 1 of the points: (4, -1)
y – -1 = -2(x – 4)
y + 1 = -2x + 8
y = -2x + 7
3
6
2
3. Through (5, 0) and (-3, 2)
5 - 3-
0 - 2 m
4
1 -
8-
2
Choose one Point and Substitute. (5, 0)
y – 0 = -¼(x – 5)
y = -¼ x + 1.25
4. Through (-3, -4) and (6, 11)
3- -6
4- - 11 m
9
15
Choose point: (-3, -4)
)3(3
54 xy
)3(3
5 4 xy
5 3
5 4 xy
13
5 xy
3
5
Writing the Equation given the Graph
1. Find the y-intercept (b)
2. Find the Slope (m =
3 Substitute m and b into y = mx + b
Write the equation of the line represented in the graph below.
m = -
b = 3
y =
On Your Own.
1. Write the equation of the line with a slope of ¾ and a y-intercept of -1.
y = ¾ x – 1
2. Write the equation of the line with a slope of 4 and goes through the point (1, -3). Write your answer in slope-intercept form.
y = 4x – 7
Homework
Worksheet 1.3