1. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
Find the rate of change of the data in each table.
Simplify each expression.
4. –3(x – 5) 5. 5(x + 2) 6. – (x – 6) 4 9 2 5 8 11 –2 –8
–14 x y –3 –5 –1 1 3 –4 10
7.5
2.5 –6
–11
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2. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
1. Use points (2, 4) and (5, –2). rate of change = = = –2
2. Use points (–3, –5) and (–1, –4). rate of change = = = =
3. Use points (10, 4) and (7.5, –1). rate of change = = = = 2
4. –3(x – 5) = –3x – (–3)(5) = –3x + 15
5. 5(x + 2) = 5x + 5(2) = 5x + 10
6. – (x – 6) = – x – (– )(6) = – x + 4 9 8 3
–5 + 4
–3 + 1
4 – (–2)
2 – 5
4 – (–1 )
10 – 7.5
–5 – (–4)
–3 – (–1)
4 + 1
2.5 5 –1 –2 6 –3 1 2
Solutions
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3. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4 1 3
Graph the equation y – 2 = (x – 1). 1 3
The equation of a line that passes through (1, 2) with slope .
Start at (1, 2). Using the slope, go up 1 unit and right 3 units to (4, 3).
Draw a line through the two points.
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4. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
Write the equation of the line with slope –2 that passes through the point (3, –3).
y – y1 = m(x – x1)
Substitute (3, –3) for (x1, y1) and –2 for m.
y – (–3) = –2(x – 3)
Simplify the grouping symbols.
y + 3 = –2(x – 3)
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5. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
Write equations for the line in point-slope form and in
slope-intercept form.
The slope is – . 1 3
Step 1  Find the slope.
= m
y2 – y1
x2 – x1
4 – 3
–1 – 2
= –
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6. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
(continued)
Step 2  Use either point to write the the equation in point-slope form.
Use (–1, 4).
y – y1 = m(x – x1)
y – 4 = – (x + 1) 1 3
Step 3  Rewrite the equation
from Step 2 in slope–
intercept form.
y – 4 = – (x + 1)
y – 4 = – x –
y = – x + 3 1 3 2
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7. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
Is the relationship shown by the data linear? If so, model the data with an equation.
Step 1  Find the rate of change for
consecutive ordered pairs. –2 –1 –6 –3
= 2 3 6 2 –1 –3 4 –2 –6 x y
–1( ) –2
–3( ) –6
–2( ) –4
The relationship is linear.
The rate of change is 2.
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8. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
(continued)
Step 2 Use the slope 2 and a point (2,4) to write an equation.
y – y1 = m(x – x1) Use the point-slope form.
y – 4 = 2(x – 2) Substitute (2, 4) for (x1, y1) and 2 for m.
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9. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
Is the relationship shown by the data linear? If so, model the data with an equation.
Step 1  Find the rate of change for
consecutive ordered pairs. 1 2
= 1 – / –2 –1 1 2 x y
1 ( ) 1
2 ( ) 1
The relationship is not linear.
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10. Point-Slope Form and Writing Linear Equations
ALGEBRA 1 LESSON 6-4
1. Graph the equation y + 1 = –(x – 3).
2. Write an equation of the line with
slope – that passes through
the point (0, 4).
3. Write an equation for the line that
passes through (3, –5) and (–2, 1) in
Point-Slope form and Slope-Intercept
form.
4. Is the relationship shown by the data
linear? If so, model that data with an
equation. 2 3
y – 4 = – (x – 0), or y = – x + 4 2 3
–10 –7 5 20 –3 –1 x y 6 5 7
y + 5 = – (x – 3); y = – x – 2 5
yes; y + 3 = (x – 0)
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