2.4 Writing Linear 2.4 Writing Linear EquationsEquationsUsing point-slope formUsing point-slope form

Slope-intercept form of a linear equations

y = mx +b

Remember m is slope

and b is the y intercept

If we are given points, then we will have to find the slope.

21

21

xx

yym

Write the equation in Slope-Intercept form

The line has a slope of -3/5 and passes through (5, -2).

Write the equation in Slope-Intercept form

The line has a slope of -3/5 and passes through (5, -2).

So x = 5 and y = -2 also m = -3/5.

- 2 = -3/5(5) + b Must find b

Write the equation in Slope-Intercept form

The line has a slope of -3/5 and passes through (5, -2).

So x = 5 and y = -2 also m = -3/5.

- 2 = -3/5(5) + b Must find b

- 2 = -3 + b Add 3

Write the equation in Slope-Intercept form

The line has a slope of -3/5 and passes through (5, -2).

So x = 5 and y = -2 also m = -3/5.

- 2 = -3/5(5) + b Must find b

- 2 = -3 + b Add 3

1 = b

Write the equation in Slope-Intercept form

The line has a slope of -3/5 and passes through (5, -2).

So x = 5 and y = -2 also m = -3/5. 1 = b

So the equation is written as

y = -3/5 x + 1

Write the equation in Slope-Intercept form

Given the points (2, - 3) and (- 3, 7).

What do you need first?

Write the equation in Slope-Intercept form

Given the points (2, - 3) and (- 3, 7).

What do you need first?

Slope: the formula is

21

21

xx

yym

Write the equation in Slope-Intercept form

Given the points (2, - 3) and (- 3, 7).

m = ( - 3) – (7) = -10 = -2 ( 2 ) – ( - 3) 5

Now we can use either point to find “b”Lets use ( -3, 7)

7 = - 2( - 3) + b7 = 6 + b1 = b With m and b y = - 2x + 1

Point slope form

Here we do not have to solve for b

Given a point and a slope, we can write an equation. Lets use the points from the last problem (2, - 3) and (- 3, 7). The slope of the line was -2.

Point slope form

Given a point and a slope, we can write an equation. (2, - 3) and (- 3, 7) and slope of the line -2.

Point-slope Formula

y – y1 = m(x – x1)

Filling in using a point and slope we have the equation

y – 7 = -2(x – (-3)) or y – (- 3) = - 2(x – 2)

Point slope form

Which one is right, lets solve for y in both

y – 7 = -2(x – (-3)) or y – (- 3) = - 2(x – 2)

y – 7 = -2x – 6 y + 3 = -2x + 4

y = - 2x + 1 y = - 2x + 1

Since the equations are the same it does not matter which point we use.

Using point-slope with parallel or perpendicular lines

Write an equation parallel to the line

y = 3x – 4

and passes through the point (2, - 4).

The slope is 3;

y – ( - 4) = 3(x – 2)

Using point-slope with parallel or perpendicular lines

Write an equation parallel to the line

y = 3x – 4

and passes through the point (2, - 4).

The slope is 3;

y – ( - 4) = 3(x – 2)

y + 4 = 3x - 6

Using point-slope with parallel or perpendicular lines

Write an equation parallel to the line

y = 3x – 4

and passes through the point (2, - 4).

The slope is 3;

y – ( - 4) = 3(x – 2)

y + 4 = 3x – 6

y = 3x - 10

Using linear equation in a word problem.

As a part-time salesperson, Jean Stock is paid a daily salary plus commission. When her sales are $100, she makes $58. When her sales are $300, she makes $78.

Write the linear equation to model this situation.

Using linear equation in a word problem.

her sales are $100, she makes $58 (100,58). When her sales are $300, she makes $78 (300, 78).

Find slope 78 – 58 = 20 = 0.1

300 – 100 200What is her daily Salary? (if she sales nothing)

Using linear equation in a word problem.

What is her daily Salary? (if she sales nothing)

What is her commission rate?If she sales $100, she makes $58The slope of the line is 0.1

y – 58 = 0.1(x – 100)y – 58 = 0.1x - 10y = 0.1x + 48

y = 0.1x + 48

So she earns $48 for just being there. Commission rate is 0.1 or 10%

What would she earn if she sold $500?

y = 0.1x + 48

So she earns $48 for just being there. Commission rate is 0.1 or 10%

What would she earn if she sold $500?

y =0.1(500) + 48

y = 50 + 48

y = $98

HomeworkHomework

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#13 – 17 odd,21, 22#13 – 17 odd,21, 22

23 – 37 odd,23 – 37 odd,

49, 50 49, 50

HomeworkHomework

Page 78 – 80 Page 78 – 80

#14 – 18 even#14 – 18 even

24 – 38 odd,24 – 38 odd,

41 - 43 41 - 43