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2.4 Writing the Equation of a Line

2.4 Writing the Equation of a Line. Review of Slope-Intercept Form. The slope-intercept form of a linear equation is y = mx + b. m represents the slope b represents the y-intercept. Review of Slope-Intercept Form. Name the slope and y-intercept of each equation :. y = -4 x + 3

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2.4 Writing the Equation of a Line

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  1. 2.4 Writing the Equation of a Line

  2. Review of Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m represents the slope b represents the y-intercept

  3. Review of Slope-Intercept Form Name the slope and y-intercept of each equation: y = -4x + 3 y = 5 – x 8x + y = 4x - 2y =10 y = x y = 5 m = -4, b =3 m = - , b = 5 Rewrite as y = -8x , m = -8, b = Rewrite as y = 2x - 5, m = 2, b = -5 Rewrite as y = x + 0, m = , b = 0 Rewrite as y = 0x + 5, m = 0, b = 5

  4. Write the equation of a line given... 1. Slope and y-intercept 2. Graph 3. Slope and one point 4. Two points 5. x - and y-intercepts

  5. m = -3, b = 1 m = -2, b = -4 m = 0, b = 10 m = 1, b = 0 m = 0, b = 0 Find the Equation of the LineGiven the Slope and y-intercept • Substitute m and b intoy = mx + b y = -3x + 1 y = -2x - 4 y = 0x + 10, y = 10 y = 1x + 0, y = x y = 0x + 0, y = 0

  6. Find the Equation of a LineGiven the Graph • Find the y-intercept from the graph. • Count the slope from the graph. • To write the equation of the line, substitute the slope and y-intercept in the slope-intercept form of the equation.

  7. +2 +3 x y Example 1 • b = -3 • m = • y = x - 3

  8. -2 +1 x y Example 2 • b = 1 • m = • y = x + 1

  9. x y Example 3 • b = 4 • m = 0/1= 0 • y = 0x + 4, y = 4

  10. Find the Equation of a LineGiven the Point and the Slope • Use the Point-Slope Formula: • is the given point • Substitute m and into the formula

  11. Example • Write the equation of the line with slope = -2 and passing through the point (3, -5). • Substitute m and into the Point-Slope Formula.

  12. Find the Equation of the LineGiven Two Points • Calculate the slope of the two points. • Use one of the points and the slope to substitute into the Point-Slope formula.

  13. Example • Write the equation of the line that goes through the points (3, 2) and (5, 4).

  14. Find the Equation of the LineGiven the x- and y - intercepts • Write the intercepts as ordered pairs. The x-intercept 4 is the ordered pair (4, 0). The y-intercept -2 is the ordered pair (0, -2). • Calculate the slope. • Substitute the slope and the y-intercept (b) into the slope-intercept formula.

  15. Example Write the equation of the line with x-intercept 3 and y-intercept 2. x-intercept 3 = (3, 0); y-intercept 2 = (0, 2) Slope: y = mx + b

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