1. Point-Slope Form 4-7 Warm Up Lesson Presentation Lesson Quiz
Holt Algebra 1
Holt McDougal Algebra 1

2. Objectives
Graph a line and write a linear equation using point-slope form.
Write a linear equation given two points.

4. Additional Example 1A: Writing Linear Equations in Point-Slope Form
Write an equation in point slope form for the line with the given slope that contains the given point.
y – y1 = m (x – x1)
Write the point-slope form.

5. Additional Example 1B: Writing Linear Equations in Point-Slope Form
Write an equation in point slope form for the line with the given slope that contains the given point.
slope = –4; (0, 3)
y – y1 = m(x – x1)
Write the point-slope form.
Substitute –4 for m, 0 for x1 and 3 for y1.
y – 3 = –4(x – 0)
y – 3 = –4(x – 0)

6. Additional Example 1C: Writing Linear Equations in Point-Slope Form
Write an equation in point slope form for the line with the given slope that contains the given point.
slope = 1; (–1, –4)
y – y1 = m(x – x1)
Write the point-slope form.
Substitute 1 for m, –1 for x1, and –4 for y1.
y – (–4) = 1(x – (–1))
Rewrite subtraction of negative numbers as addition.
y + 4 = 1(x + 1)

7. Check It Out! Example 1b
Write an equation in point slope form for the line with the given slope that contains the given point.
slope = 0; (3, –4)
y – y1 = m(x – x1)
Write the point-slope form.
Substitute 0 for m, 3 for x1 and –4 for y1.
y – (–4) = 0(x – 3)
Rewrite subtraction of negative numbers as addition.
y + 4 = 0(x – 3)

8. Additional Example 2A: Using Point-Slope Form to Graph
Graph the line described by the equation.
y – 1 = 2(x – 3)
(2,5)
y – 1 = 2(x – 3) is in the form y – y1= m(x – x1).
(1,3)
The line contains the point (3, 1).
Step 1 Plot (3, 1).
Step 2 Count 2 units up and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.

9. Additional Example 2B: Using Point-Slope Form to Graph
Graph the line described by the equation.
(2,7)
y – 4 = (x – (–2)) is in the
form y – y1= m(x – x1).
(-2,4)
The line contains the point (–2, 4).
slope: m =
Step 1 Plot (–2, 4).
Step 2 Count 3 units up and 4 units right and plot another point.
Step 3 Draw the line connecting the two points.

10. Additional Example 2C: Using Point-Slope Form to Graph
Graph the line described by the equation.
y + 3 = 0(x – 4)
y – (–3) = 0(x – 4) is in the form y – y1= m(x – x1).
The line contains the point (4, –3).
slope: m = 0
Step 1 Plot (4, –3).
Step 2 There slope is 0. Every value of x will be at y = –3.
Step 3 Draw the line connecting the points.

11. Check It Out! Example 2a
Graph the line described by the equation.
y + 2 = –(x – 2)
y – (–2) = –1(x − 2) is in the form y – y1 = m(x – x1).
The line contains the point (2, –2).
Step 1 Plot (2, –2).
Step 2 Count 1 unit down and 1 unit right and plot another point.
Step 3 Draw the line connecting the points.

12. Graph the line described by the equation.
Check It Out! Example 2b
Graph the line described by the equation.
y + 3 = –2(x – 1)
y – (–3) = –2(x − 1) is in the form y – y1= m(x – x1).
The line contains the point (1, –3).
(0,-1)
slope: m = –2
(1,-3)
Step 1 Plot (1, –3).
Step 2 Count 2 units up and 1 unit left and plot another point.
Step 3 Draw the line connecting the points.

13. Additional Example 3A: Writing Linear Equations in Slope-Intercept Form
Write the equation that describes each line in slope-intercept form.
Slope = 3, (–1, 4) is on the line.
Step 1 Write the equation in point-slope form:
y – y1 = m(x – x1)
y – 4 = 3[x – (–1)]
Step 2 Write the equation in slope-intercept form by solving for y.
Rewrite subtraction of negative numbers as addition.
y – 4 = 3(x + 1)
Distribute 3 on the right side.
y – 4 = 3x + 3
Add 4 to both sides.
y = 3x + 7

14. Additional Example 3B: Writing Linear Equations in Slope-Intercept Form
Write the equation that describes the line in slope-intercept form.
(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.
y – y1 = m(x – x1)
y – (–3) = 2(x – 2)
Choose (2, –3).

15. Additional Example 3B Continued
Write an equation in slope-intercept form for the line through the two points.
(2, –3) and (4, 1)
Step 3 Write the equation in slope-intercept form.
y + 3 = 2(x – 2)
y + 3 = 2x – 4
– –3
y = 2x – 7