Find the slope-intercept form, given a linear equation Graph the line described the slope-intercept...

Find the slope-intercept form, given a linear equation

Graph the line described the slope-intercept form

What is the relationship between the slopes of parallel lines?

What is the relationship between the slopes of perpendicular lines?

Recall the point-intercept form of linear equation.

y – y1

----- = m x – x1

y – y1 = m (x – x1)

E.g., y – 1 = 3(x – 2)

• y – y1 = m(x – x1)

• Suppose (x1, y1) = (0, b)Then

• y – y1 = m(x – x1)y – b = mxy = mx + b

m = slopeb = y-intercept

• y = ½ x + 3

m = ½b = 3

• y = 2 x – 5

m = 2b = -5

• Find the slope and the y-intercept of the line.

a) 2x + 5y = 3 5y = -2x + 3 y = (-2/5)x + 3/5 m = -2/5 b = 3/5

b) 3x – 4y = 9

Suppose a line has a slope of 5 and passes through (-2, 9). Write the slope-intercept form of the equation for the line.

Solutiony = mx + b9 = 5(-2) + b19 = b

y = 5x + 19

Suppose that a line passes through the following 2 points: (-3, 4), (5, -8).Write the slope-intercept form of the equation of the line.

Solution:m = (-8 – 4)/(5 – (-3)) = -12/8 = -3/2y = mx + b4 = (-3/2)(-3) + b4 = 9/2 + bb = -1/2

y = (-3/2)x – 1/2

y = (4/3)x – 2

m = 4/3b = -2

Find the slope and the y-intercept of the line: 2(x – 3) = –3(y + 5). Graph the equation.

Solution 2x – 6 = -3y – 15

3y = -2x – 9y = (-2/3)x – 3

m = -2/3b = -3

Show that the lines represented by 4x + 8y = 16 and x = 6 – 2y are parallel.

Two lines are parallel if their slopes are equal4x + 8y = 16 x = 6 – 2y8y = -4x + 16 2y = -x + 6y = -(1/2)x = 2 y = (-1/2) + 3

2 and -1/2 are negative reciprocals of each other.

So are 3/4 and -4/3. What is the negative reciprocal of 3/5?

If two lines are perpendicular to each other, their slopes are negative reciprocals

If the slopes of two lines are negative reciprocals, the lines are perpendicular.

Write an equation of the line passing through (–3, 2) and parallel to the line y = 8x – 5.

Solution:Solve for b, in y = mx + b

A company buys a $12,500 computer with an estimated life of 6 years. The computer can then be sold as scrap for an estimated salvage value of $500. If y represents the value of the computer after x years of use and y and x are related by the equation of a line,

a. Find an equation of the line and graph it.b. Find the value of the computer after 2 years.c. Find the economic meaning of the y-intercept of the

line.d. Find the economic meaning of the slope of the line.