Point-Slope Form 4.5 1.Use point-slope form to write the equation of a line. 2.Write the equation of a line parallel to a given line. 3.Write the equation.

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Presentation transcript:

Point-Slope Form Use point-slope form to write the equation of a line. 2.Write the equation of a line parallel to a given line. 3.Write the equation of a line perpendicular to a given line.

Practice …… 1. Write in standard form:2. Write in standard form: 3. Write in standard form:4. Write in standard form:

Practice …… 1. Write in standard form:2. Write in standard form: 3. Write in slope-intercept form:4. Write in slope-intercept form:

Objective 1 Use point-slope form to write the equation of a line.

Point Slope Form Given two points (x 1, y 1 ) and (x, y) Use whenever you want to write an equation! Need to know a point and a slope.

Write the equation of a line with a slope of 5 and passing through the point (3, 12) in slope-intercept form. y – y 1 = m(x – x 1 ) m = 5, x 1 = 3, y 1 = 12 Write the equation in standard form. Slope: y – y 1 = m(x – x 1 ) y – 12 = 5(x – 3) y – 12 = 5x – 15 Distribute. y = 5x – 3 Add 12 to both sides to isolate y. (3, 12) Point: 5 y – 12 = 5x – 15 -5x + y -12 = x + y = -3 5x – y = 3

Write the equation of a line passing through (-1, -5) and (-4, 1) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point: Slope: (-1, -5) slope-interceptstandard form

Write the equation of a line with a slope of and passing through the point (-3, 5) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point:Slope: (-3, 5) slope-interceptstandard form

Write the equation of a line passing through (2, -4) and (3, -4) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point:Slope: (2, -4) Horizontal line Intersects only the y-axis. Equation has only a y. y = -4

Write the equation of a line passing through (-2, 5) and (-2, -6) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point: Slope: (-2, 5) Vertical line Intersects only the x-axis. Equation has only an x. x = -2

Objective 2 & 3 Write the equation of a line parallel to a given line. Write the equation of a line perpendicular to a given line.

Parallel Lines The slopes of parallel lines are equal. y = 2x + 1 y = 2x – 3

Perpendicular Lines The slopes of perpendicular lines are negative reciprocals.

The only way to determine if lines are parallel or perpendicular is to compare the slopes.

Parallel or Perpendicular? Parallel m = 3 Neither m = 5 m = -5 Perpendicular horizontal vertical Perpendicular

y – y 1 = m(x – x 1 ) y – (  5) = –3(x – 1) y + 5 = –3x + 3 y = –3x – 2 (1, -5) Write the equation of a line that passes through (1, –5) and parallel to y = –3x + 4. Write the equation in slope-intercept form. y – y 1 = m(x – x 1 )Need a point and slope m = -3

Write the equation of a line that passes through (3, 7) and perpendicular to 5x + 2y = 3. Write the equation in standard form. (3, 7) y – y 1 = m(x – x 1 )Need a point and slope

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write the equation of the line in slope-intercept form given m =  2 and the point (4,  5). a) y =  2x – 3 b) y = 2x + 3 c) y =  2x + 3 d) y =  2x – 5

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write the equation of the line in slope- intercept form given m =  2 and the point (4,  5). a) y =  2x – 3 b) y = 2x + 3 c) y =  2x + 3 d) y =  2x – 5

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the equation of the line connecting the points (4,  3) and (  1, 7) in slope- intercept form? d) a) y =  2x + 5 b) y = 2x + 5 c) y =  2x – 5

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the equation of the line connecting the points (4,  3) and (  1, 7)? a) y =  2x + 5 b) y = 2x + 5 c) y =  2x – 5 d)

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the relationship between the two lines? 5x – 3y = 11 3x + 5y = 8 a) parallel b) perpendicular c) neither

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the relationship between the two lines? 5x – 3y = 11 3x + 5y = 8 a) parallel b) perpendicular c) neither