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Section 5-1 Write Linear Equations in Slope-Intercept Form

Section 5-1 Write Linear Equations in Slope-Intercept Form. Objective: Students will write equations in slope-intercept form. Standard: A.CED.2 , F.IF.2. Slope Intercept Form: y = m x + b or f(x) = m x + b m = slope b = y-intercept. Example 1

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Section 5-1 Write Linear Equations in Slope-Intercept Form

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  1. Section 5-1Write Linear Equationsin Slope-Intercept Form Objective: Students will write equations in slope-intercept form. Standard: A.CED.2 , F.IF.2

  2. Slope Intercept Form: y = mx + b or f(x) = mx + b m = slope b = y-intercept

  3. Example 1 Write an equation of the line with a slope of 4 and a y-intercept of -3. y = mx + b • Substitute 4 for m and -3 for b. y = 4x -3

  4. Example 2 Write an equation of the line shown. Step 1: Find the slope: (0,2) m = -3 (4, -1) 4 Step 2: Write an equation of the line. The line crosses the y-axis at (0,2). So, the y-intercept is 2. Use slope-intercept form and substitute -¾ for m & 2 for b. y = -¾x + 2

  5. Example 3 Write the equation of the line passing thru the 2 points: (0, 4) and (6, 13). x1,y1 x2,y2 Step 1:Calculate the slope of the line that passes through (0,4) and (6, 13). m = y2 – y1= x2 – x1 13 – 4 6 – 0 = 9 6 = 3 2 Step 2:Solve for b. Substitute one point and the slope into y = mx + b Hint: Use the point that has a ZERO in it! m = and use (0, 4) x = 0 and y = 4 y = mx + b Substitute values 4 = ( )(0) + b Solve for b. 4 = 0 + b 4 = b y = x + 4 Step 3: Write an equation: y = mx + b Substitutefor mand 4 for b.

  6. Example 4 Write an equation for the linear function f with the values f(0) = 3 and f(-4) = 11. Step 1:Write two ordered pairs f(0) = 3 (0, 3) f(-4) = 11 (-4, 11) x1,y1 x2,y2 Step 2:Calculate the slope of the line that passes through the (0,3) and (-4, 11). m = y2 – y1= 11 – 3 = 8 = -2 x2 – x1-4 – 0 -4 Step 3:Solve for b. Substitute one point and the slope into y = mx + b Hint: Use the point that has a ZERO in it! m = -2 and use (0, 3) x = 0 and y = 3 y = mx + b Substitute values 3 = ( -2 )(0) + b Solve for b. 3 = 0 + b 3 = b Step 4: Write an equation: y = mx + b Substitute-2formand 3 for b. y = -2x + 3 Written as a function: f(x) = -2x + 3

  7. Example 5 Write an equation of the line that passes through the point (6, 3) and has a slope of -2. Step 1: Identify the slope. Use slope formula if needed. m = -2 Step 2: Find the y-intercept. Substitute one point and the slope into y = mx + b. Solve for b! m = -2 and (6, 3) x = 6 and y = 3 y = mx + b Substitute values 3 = ( -2 )(6) + b Solve for b. 3 = -12 + b +12 +12 15 = b Step 3: Write the equation in slope intercept form (y = mx + b) y = -2x + 15

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