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Forms of a linear equation

Forms of a linear equation. Slope-intercept Form y = mx + b Standard Form Ax + By = C Point-Slope Form y – y 1 = m(x – x 1 ). If given the slope and y-intercept,. use slope-intercept form. Example m = 5, b = 7. 5. 7. y = ___ x + ___. (B8) Writing the Equation of a Line.

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Forms of a linear equation

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  1. Forms of a linear equation Slope-intercept Form y = mx + b Standard Form Ax + By = C Point-Slope Form y – y1 = m(x – x1)

  2. If given the slope and y-intercept, use slope-intercept form. Example m = 5, b = 7 5 7 y = ___ x + ___

  3. (B8) 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

  4. 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

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

  6. 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

  7. 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.

  8. +2 +3 x y Example 1 • b = -3 • m = • y = x - 3

  9. -2 +1 x y Example 2 • b = 1 • m = • y = x + 1

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

  11. 3. 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.

  12. 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

  13. 4. Find the Equation of the LineGiven the Slope and a Point If given the a point and the slope, Step 1 Use slope-intercept form. Substitute –2 for m, 5 for x, and –8 for y; then simplify to find the value of b. y = mx + b –8 = –2(5) + b –8 = –10 + b 2 = b Example m = –2, contains (5, –8) Step 2 Substitute –2 for m, and 2 for b. y = –2x + 2

  14. 5. Find the Equation of the LineGiven Two Points If given two points, First, find the slope using the slope formula. Example contains (5, –8) and (2, 7) m = 15 –3 m = –5 m = 7 – -8 2 – 5

  15. If given two points, Then use the slope and EITHER point to work like the previous example. y = mx + b 7 = -5(2) + b 7 = -10 + b b = 17 m = –5, contains (5, –8) and (2, 7) y = –5x + 17

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

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