Warm Up.

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Objective - To graph linear equations using the slope and y-intercept.

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Presentation transcript:

Warm Up

To be able to write a linear equation. Today’s Objective To be able to write a linear equation.

y = mx + b Slope-intercept form of the equation: Recall #1 Slope-intercept form of the equation: y = mx + b m is slope and b is the y-intercept.

Recall #1 y = mx + b y = 3x + 2 3 is slope and 2 is the y-intercept.

Y = 3x + 2 Slope = 3/1 Y y-intercept X

Recall #2 Slope Formula: m = y2 - y1 x2 - x1

(1, 4) and (2, 3) (x1, y1) & (x2, y2) m = 3 - 4 2 - 1 Recall #2 Slope Formula: m = y2 - y1 x2 - x1

Recall #2 m = 3 - 4 2 - 1 m = -1 1 m = -1

Write a linear Equation If f(2) = 5 and f(6) = 3 f(2) = 5 when x =2 & y = 5 (2,5) f(6) = 3 when x = 6 & y = 3 (6,3)

(2,5) & (6,3) When x = 2, f(x) = 5 f(x) When x = 6, f(x) = 3 X

(2, 5) and (6, 3) (x1, y1) & (x2, y2) m = 3 - 5 6 - 2 Step 1 find the slope (2, 5) and (6, 3) (x1, y1) & (x2, y2) m = 3 - 5 6 - 2 Slope Formula: m = y2 - y1 x2 - x1

Step 1 find the slope m = 3 - 5 6 - 2 m = -2 4 m = -1/2

y = mx + b (2,5) and (6,3) 5 = -1/2(2) + b 5 = -1 + b 6 = b Step 2 y = mx + b y = mx + b (2,5) and (6,3) 5 = -1/2(2) + b 5 = -1 + b 6 = b

y = -1/2x + 6 is the equation of the line. Finish If m = -1/2 and b = 6, then: y = -1/2x + 6 is the equation of the line.

Y = -1/2x + 6 f(x) X

Your Turn Write an equation of the line for: f(2) = -2 and f(-4) = 1 Step 1 find the slope Step 2 use y = mx + b to find the b value.

f(2) = -2 and f(-4) = 1 (2, -2) and (-4, 1) Slope = y2 - y1 x2 - x1 Step 1 find the slope f(2) = -2 and f(-4) = 1 (2, -2) and (-4, 1) Slope = y2 - y1 x2 - x1

(2, -2) and (-4, 1) Slope = 1 - -2 -4 - 2 Slope = 3 -6 Step 1 find the slope (2, -2) and (-4, 1) Slope = 1 - -2 -4 - 2 Slope = 3 -6 m = -1/2

y = mx + b (2,-2) and (-4,1) -2 = -1/2(2) + b -2 = -1 + b -1 = b Step 2 y = mx + b y = mx + b (2,-2) and (-4,1) -2 = -1/2(2) + b -2 = -1 + b -1 = b

y = -1/2x + -1 is the equation of the line. Finish If m = -1/2 & b = -1, then: y = -1/2x + -1 is the equation of the line.

Classwork See Side Board