2.4 Writing Linear EquationsUsing point-slope form

Slope-intercept form of a linear equations y = mx +bRemember m is slope and b is the y intercept

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

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) + bMust 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) + bMust find b- 2 = -3 + bAdd 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) + bMust find b- 2 = -3 + bAdd 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

Write the equation in Slope-Intercept form Given the points (2, - 3) and (- 3, 7).

m = ( - 3) (7)= -10 = -2 ( 2 ) ( - 3) 5Now we can use either point to find bLets use ( -3, 7)7 = - 2( - 3) + b7 = 6 + b1 = bWith m and by = - 2x + 1

Point slope formHere 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 formGiven a point and a slope, we can write an equation. (2, - 3) and (- 3, 7) and slope of the line -2. Point-slope Formulay y1 = m(x x1)Filling in using a point and slope we have the equationy 7 = -2(x (-3)) or y (- 3) = - 2(x 2)

Point slope formWhich one is right, lets solve for y in bothy 7 = -2(x (-3)) or y (- 3) = - 2(x 2)y 7 = -2x 6 y + 3 = -2x + 4 y = - 2x + 1 y = - 2x + 1Since the equations are the same it does not matter which point we use.

Using point-slope with parallel or perpendicular linesWrite 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 linesWrite 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 linesWrite 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 slope78 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 0.1y 58 = 0.1(x 100)y 58 = 0.1x - 10y = 0.1x + 48

y = 0.1x + 48So 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 + 48So 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) + 48y = 50 + 48y = $98

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