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Writing Linear Equations: Slope-Intercept Form, Parallel & Perpendicular Lines

In this lesson on writing linear equations, you'll learn how to write equations in slope-intercept form given the slope and y-intercept, a point with the slope, or two points. We’ll cover writing equations for parallel and perpendicular lines, using the formula ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. You'll practice finding equations of lines that pass through given points, as well as explore the characteristics of parallel and perpendicular lines. Solutions will be provided for practice exercises.

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Writing Linear Equations: Slope-Intercept Form, Parallel & Perpendicular Lines

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  1. Chapter 2.4 Writing Linear Equations

  2. By the end of this lesson you will be able to: • Write an equation in slope-intercept form when given: slope and a y-intercept a point and the slope two points • Write an equation of a parallel line • Write an equation of a perpendicular line

  3. Slope-Intercept Form: Y = mx + b B = y-intercept M = slope of the line

  4. Writing equations of Lines: • Given slope of -8 and passes through (2,4) • Take the equation y=mx+b and substitute the -8 in for “m” • Y = (-8)x + b • To find the value of “b” – take the value of x and y from the point and substitute • (4) = (-8)(2) +b • b = 20 • Y = -8x + 20

  5. You Try! • Write the equation of the line with a slope of 3 and passing through (0, -5).

  6. Equations – given two points: • Given two points (4,1) and (7,7) • Find the slope using the slope formula • Plug 2 in for “m” • Pick one of the points to get the values for the x and y • Once you get the value for “b” then rewrite the equation • Y = 2x - 7 (1) = (2)(4) + b b = -7

  7. You Try! • Write the equation of the line that passes through the points (4, 8) and (-2, 10).

  8. Parallel Lines: • Parallel Lines have the same slope • Write an equation that is parallel to y=3x+2 and passes through (0,2) • The new line would have the same slope, so m=3 • Take the x and y from the point and find “b”

  9. You Try! • Write an equation that is parallel to y=1/2x + 4 and passes through (-8, 3)

  10. Perpendicular Lines: • Perpendicular Lines have slopes that are opposite-reciprocal • Write an equation that is perpendicular to y= -½x +2 and passes through (8,2) • The new line’s slope would be 2 • Take the x and y value to find b • Then rewrite the new equation

  11. You Try! • Write and equation that is perpendicular to y = - 1/3x – 4 and passes through (2, 5)

  12. Tonight’s Homework: Page 79 (23-37 odd)

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