1. Objectives
Graph lines and write their equations in slope-intercept and point-slope form.
Classify lines as parallel, intersecting, or coinciding.

2. The equation of a line can be written in many different forms
The equation of a line can be written in many different forms. The point-slope and slope-intercept forms of a line are equivalent. Because the slope of a vertical line is undefined, these forms cannot be used to write the equation of a vertical line.

4. Example 1A: Writing Equations In Lines
Write the equation of each line in the given form.
the line with slope 6 through (3, –4) in point-slope form
y – y1 = m(x – x1)
Point-slope form
y – (–4) = 6(x – 3)
Substitute 6 for m, 3 for x1, and -4 for y1.
y – (–4) = 6(x – 3)
Don’t simplify

5. Write the equation of each line in the given form.
Check It Out! Example 1b
Write the equation of each line in the given form.
the line through (–3, 2) and (1, 2) in
point-slope form
Find the slope.
y – y1 = m(x – x1)
Point-slope form
Pick either point. I chose the 2nd. Substitute 0 for m, 1 for x1, and 2 for y1.
y – 2 = 0(x – 1)
y – 2 = 0(x – 1)
Don’t simplify.

6. A line with y-intercept b contains the point (0, b).
A line with x-intercept a contains the point (a, 0).
Remember!

7. Example 1C: Writing Equations In Lines
Write the equation of each line in the given form.
the line with the x-intercept 3 and y-intercept –5 in point slope form
Use the point (3,-5) to find the slope.
y – y1 = m(x – x1)
Point-slope form
y – 0 = (x – 3) 5 3
Pick a point. I chose the first. Substitute for m, 3 for x1, and 0 for y1. 5 3
y – 0 = (x – 3) 5 3
Don’t simplify.

8. Check It Out! Example 1a
Write the equation of each line in the given form.
the line with slope ½ through (10, 4) in
slope-intercept form
y = mx + b
Slope intercept form
4 = ½(10) + b
Substitute 0 for m, 10 for x, and 4 for y.
4 = 5 + b
-1 = b
Solve for b
Write in slope-intercept form using m = ½ and b = -1.
y = ½x – 1

9. Example 1B: Writing Equations In Lines
Write the equation of each line in the given form.
the line through (–1, 0) and (1, 2) in
slope-intercept form
Find the slope.
Slope-intercept form
y = mx + b
2 = 1(1) + b
Pick a point. I chose the 2nd. Substitute 1 for m, 1 for x, and 2 for y. Solve for b.
1 = b
Write in slope-intercept form using m = 1 and b = 1.
y=mx+b  y = x + 1

10. Example 2A: Graphing Lines
Graph each line.
The equation is given in the slope-intercept form, with a slope of and a y-intercept of 1. Plot the point (0, 1) and then rise 1 and run 2 to find another point. Draw the line containing the points.
(0, 1)
rise 1
run 2

11. Check It Out! Example 2a Graph each line. y = 2x – 3
The equation is given in the slope-intercept form, with a slope of and a y-intercept of –3. Plot the point (0, –3) and then rise 2 and run 1 to find another point. Draw the line containing the points.
(0, –3)
rise 2
run 1

12. Example 2B: Graphing Lines
Graph each line.
y – 3 = –2(x + 4)
The equation is given in the point-slope form, with a slope of through the point (–4, 3). Plot the point (–4, 3) and then rise –2 and run 1 to find another point. Draw the line containing the points.
(–4, 3)
rise –2
run 1

13. Check It Out! Example 2b Graph each line.
The equation is given in the point-slope form, with a slope of through the point (–2, 1). Plot the point (–2, 1)and then rise –2 and run 3 to find another point. Draw the line containing the points.
(–2, 1)
run 3
rise –2

14. Example 2C: Graphing Lines
Graph each line.
y = –3
The equation is given in the form of a horizontal line with a y-intercept of –3.
The equation tells you that the y-coordinate of every point on the line is –3. Draw the horizontal line through (0, –3).
(0, –3)