g ch03 06 - Geometry with Mr. Windle · 3x + 6 = -5y are parallel, intersect, or coincide. Both...

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I will graph lines and write their equations in slope-intercept and point-slope form.

I will classify lines as parallel, intersecting, or coinciding.

CN#6 Objectives point-slope form slope-intercept form

Vocabulary

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

Remember!

Check It Out! Example 1a

Write the equation of each line in the given form.

the line with slope 0 through (4, 6) in slope-intercept form

y = 6

y – y1 = m(x – x1)

y – 6 = 0(x – 4)

Start in Point-slope form

Substitute 0 for m, 4 for x1, and 6 for y1.

Slope-intercept form.

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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

y - 2 = 0

Find the slope.

y – y1 = m(x – x1) Point-slope form

Simplify.

Substitute 0 for m, 1 for x1, and 2 for y1.

y – 2 = 0(x – 1)

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

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

Check It Out! Example 2c

Graph each line.

y = –4

The equation is given in the form of a horizontal line with a y-intercept of –4.

The equation tells you that the y-coordinate of every point on the line is –4. Draw the horizontal line through (0, –4).

(0, –4)

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Classifying Lines   A system of two linear equations in two

variables represents two lines.

  The lines can be parallel, intersecting, or coinciding.

  Lines that coincide are the same line, but the equations may be written in different forms.

Check It Out! Example 3

Determine whether the lines 3x + 5y = 2 and 3x + 6 = -5y are parallel, intersect, or coincide.

Both lines have the same slopes but different y-intercepts, so the lines are parallel.

Solve both equations for y to find the slope-intercept form.

3x + 5y = 2

5y = –3x + 2

3x + 6 = –5y