1.1 writing linear equations
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1.1 Writing Linear Equations. Finding Slope Slope-Intercept Form Point-Slope Form. Finding Slope. The slope of the line that contains (2, 5) and (8, 1). is. Slope. Example 1: Finding Slope by Using the Slope Formula. Find the slope of the line that contains (2, 5) and (8, 1). - PowerPoint PPT PresentationTRANSCRIPT
1.1 Writing Linear Equations
Finding SlopeSlope-Intercept Form
Point-Slope Form
Finding Slope
Example 1: Finding Slope by Using the Slope FormulaFind the slope of the line that contains (2, 5) and (8, 1).
Use the slope formula.
Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2).
Simplify.
The slope of the line that contains (2, 5) and (8, 1)
is .
Slope
Find the slope of the line that contains (–2, –2) and (7, –2).Check It Out! Example 1a
Use the slope formula.
Substitute (–2, –2) for (x1, y1) and (7, –2) for (x2, y2).
Simplify.
The slope of the line that contains (–2, –2) and (7, –2) is 0.
= 0
Slope
Find the slope of the line that contains (5, –7) and (6, –4).Check It Out! Example 1b
Use the slope formula.
Substitute (5, –7) for (x1, y1) and (6, –4) for (x2, y2).
Simplify.
The slope of the line that contains (5, –7) and (6, –4) is 3.
= 3
Slope
Example 2A: Finding Slope from Graphs and TablesThe graph shows a linear relationship. Find the slope.
Let (0, 2) be (x1, y1) and (–2, –2) be (x2, y2).
Simplify.
Use the slope formula.
Substitute (0, 2) for (x1, y1) and (–2, –2) for (x2, y2).
Slope
Check It Out! Example 2a
The graph shows a linear relationship. Find the slope.
Simplify.
Use the slope formula.
Let (2, 2) be (x1, y1) and (4, 3) be (x2, y2).
Substitute (2, 2) for (x1, y1) and (4, 3) for (x2, y2).
Slope
Check It Out! Example 2b
Simplify.
Use the slope formula.
Let (–2, 4) be (x1, y1) and (0, –2) be (x2, y2).
Substitute (–2, 4) for (x1, y1) and (0, –2) for (x2, y2).
The graph shows a linear relationship. Find the slope.
Slope
As shown in the previous examples, slope can be positive, negative, zero or undefined. You can tell which of these is the case by looking at a graph of a line–you do not need to calculate the slope.
Slope
Example 4: Finding Slopes of Horizontal and Vertical Lines
Find the slope of each line.
You cannot divide by 0
The slope is undefined. The slope is 0.
A. B.
Slope
Slope-Intercept Form
Holt Algebra 2
2-4 Writing Linear Functions Example 1: Writing the Slope-Intercept Form of the
Equation of a LineWrite the equation of the graphed line in slope-intercept form.
Step 1 Identify the y-intercept.The y-intercept b is 1.
Holt Algebra 2
2-4 Writing Linear Functions Example 1 Continued
Step 2 Find the slope.Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units.
Slope is = = – . riserun
–34
34
3
–44
–3
Holt Algebra 2
2-4 Writing Linear Functions Example 1 Continued
Step 3 Write the equation in slope-intercept form.
y = mx + b
34y = – x + 1 m = – and b = 1. 3
4
The equation of the line is 34y = – x + 1.
Holt Algebra 2
2-4 Writing Linear Functions
Write the equation of the graphed line in slope-intercept form.
Step 1 Identify the y-intercept.The y-intercept b is 3.
Check It Out! Example 1
Holt Algebra 2
2-4 Writing Linear Functions
Step 2 Find the slope.Choose any two convenient points on the line, such as (–4, 0) and (0, 3). Count from (–4, 0) to (0, 3) to find the rise and the run. The rise is 3 units and the run is 4 units
Check It Out! Example 1 Continued
3
Slope is = . riserun
34
3 4 4
3
Holt Algebra 2
2-4 Writing Linear Functions
Step 3 Write the equation in slope-intercept form.
Check It Out! Example 1 Continued
y = mx + b
34y = x + 3 m = and b = 3. 3
4
The equation of the line is 34y = x + 3.
Point-Slope Form
Holt Algebra 1
5-7 Point-Slope FormExample 4A: Using Two Points to Write an EquationWrite an equation in slope-intercept form for the line through the two points.(2, –3) and (4, 1)Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the point-slope form.
Choose (2, –3).
y – y1 = m(x – x1)y – (–3) = 2(x – 2)
Holt Algebra 1
5-7 Point-Slope Form
Step 3 Write the equation in slope-intercept form.
y = 2x – 7–3 –3
Example 4A ContinuedWrite an equation in slope-intercept form for the line through the two points.(2, –3) and (4, 1)
y + 3 = 2(x – 2)y + 3 = 2x – 4
Holt Algebra 1
5-7 Point-Slope FormExample 4B: Using Two Points to Write an Equation
Write an equation in slope-intercept form for the line through the two points.(0, 1) and (–2, 9)Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the point-slope form.
Choose (0, 1).y – y1 = m(x – x1)y – 1 = –4(x – 0)
Holt Algebra 1
5-7 Point-Slope FormExample 4B Continued
Write an equation in slope-intercept form for the line through the two points.(0, 1) and (–2, 9)
Step 3 Write the equation in slope-intercept form.
y = –4x + 1+ 1 +1
y – 1 = –4(x – 0)y – 1 = –4x
Holt Algebra 1
5-7 Point-Slope FormCheck It Out! Example 4a
Write an equation in slope-intercept form for the line through the two points.(1, –2) and (3, 10)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the point-slope form.
Choose (1, –2).
y – y1 = m(x – x1)y – (–2) = 6(x – 1)
y + 2 = 6(x – 1)
Holt Algebra 1
5-7 Point-Slope FormCheck It Out! Example 4a Continued
Write an equation in slope-intercept form for the line through the two points.
Step 3 Write the equation in slope-intercept form.
y + 2 = 6x – 6– 2 – 2
y = 6x – 8
(1, –2) and (3, 10)
y + 2 = 6(x – 1)
Holt Algebra 1
5-7 Point-Slope FormCheck It Out! Example 4b
Write an equation in slope-intercept form for the line through the two points.(6, 3) and (0, –1)
Step 1 Find the slope.
Step 2 Substitute the slope and one of the points into the point-slope form.
Choose (6, 3).
y – y1 = m(x – x1)
Holt Algebra 1
5-7 Point-Slope FormCheck It Out! Example 4b Continued
Step 3 Write the equation in slope-intercept form.
+ 3 +3
Write an equation in slope-intercept form for the line through the two points.(6, 3) and (0, –1)
More ExamplesExample 1
Step 2: Find the slope.
More ExamplesExample 1 Continued
Notice how they gave you the y-intercept.
That means we can use slope-intercept form.
More ExamplesExample 2
Step 2: Find the slope.
More ExamplesExample 2 Continued
Notice how they didn’t give you the y-intercept.
That means we have to use point-slope form
More ExamplesExample 2 Continued
Now we need to simplify
Subtracting a negative is really adding
Add the 4 to both sides
+4 +4
More ExamplesExample 3 You Try Now
Write the equation of the lineSimply if needed
More ExamplesExample 4 You Try Now
Write the equation of the lineSimply if needed
More ExamplesAnswer Example 3
Step 2: Find the slope.
More ExamplesAnswer Example 3 Continued
Notice how they gave you the y-intercept.
That means we can use slope-intercept form.
More ExamplesAnswer Example 4
Step 2: Find the slope.
More ExamplesAnswer Example 4 Continued
Notice how they didn’t give you the y-intercept.
That means we have to use point-slope form
More ExamplesAnswer Example 4 Continued
Now we need to simplify
Subtracting a negative is really adding
Subtract the 14.2 from both sides-14.2 -14.2