A. How to Find Slope Given a Graph = Rise

DAY 2 Slope Slope - think “ steepness, hills , roofs, steps”

A. How to find slope given a graph = Rise Run

• ( 2,3)

• (4, -1) Count from one dot to the next, going vertically then horizontally.

Rise = -4 Down four units = -2 * always reduce Run 2 Right two units 1

General type of slopes

Zero slope

Positive slope Negative slope Undefined slope

B. Finding slope between two points:

Slope = Y2 – Y1 Where ( x1, y1) and ( x2, y2) are two points X2 - X1

Ex # 1 Find the slope between the points ( 2, 3 ) and ( 7, 5 ) .

M = 5 – 3 = 2 7- 2 5

Ex # 2 Find the slope between the points ( -4 , -3 ) and ( 6, -9 )

M= -9 - - 3 = - 9 + 3 = -6 = -3 * Always reduce slope to lowest terms 6 - - 4 6 + 4 10 5 DAY 3 Slope-intercept form

Slope intercept form: y = mx + b

m = slope and b = y-intercept

y-intercept is the point where the graph crosses the y axis.

Ex # 1 Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished.

A. Write an equation to find the total number of pages, P, written after any number of months.

15 pages per month is what is changing, so that is our slope.

10 pages already written is the starting point, so that is our y-intercept.

P = 15 m + 10

B. Graph the equation.

1. Put a dot on the starting point of 10. 2. Next pick a few values of m to plug in. P = 15(1) + 10 = 25 P = 15(2) +10 = 40 3. Plot these points and make a line.

C. Find the total number of pages written after 5 months.

Substitute 5 into the equation and solve for P.

P = 15(5) + 10 = 85 pages

Ex # 2 Write the equation of the line having a slope of 2 and a y-intercept of 5. Since m = 2 and b = 5 then y = 2x + 5 Ex # 3 Write the equation of the line shown in the graph.

Find slope. Count rise then run from one point to the other. m = 6/1 Find the y-intercept b = - 2

y = 6x - 2

Ex # 4 Graph the equation y = -2x + 3  Make sure your equation is solved for y before you begin.  Next find m and b. m = -2/ 1 b = 3  Then put a dot on the y-axis at b.  From the dot, count your rise then your run and put a second dot.  Connect the dots.

m = -2/ 1 b = 3 down 2 right 1

Ex # 5 Write a linear equation to model each situation.

An internet company charges $50 to install DSL plus $29.99 per month service fees.

m = 29.99 (per) b= 50 (starting point) so y = 29.99 x + 50.

 Remember per and each represent what is changing, so they are clues for the slope. Day 4 Converting from standard form to slope-intercept form.

Slope- intercept form: y= mx + b

Standard form: Ax + By = C A, B and C are integers A is not negative

 To convert between standard form and slope-intercept form, solve for y.

EX # 1 3x + 4y = 12 -3x -3x Subtract 3x from both sides 4y = -3x + 12 Write non-like terms next to each other. 4 4 4 Divide all 3 parts by the coefficient of y.

y = -3/4 x + 3

Ex # 2 2x – 6y + 9 =0 + 6y + 6y Since all terms are on the same side, move the y. 2x + 9 = 6y Divide all 3 parts by the coefficient of y. 6 6 6

1/3 x + 3/2 = y Always reduce fractions when possible.

Horizontal and Vertical Lines

Since the line crosses the y axis at -3, the equation is y = -3

Since the line crosses the x-axis at 2, the equation is x = 2 Ex # 3 a). Graph the equation X + 9 = 12 -9 -9 X = 3

b). Graph the equation 2y + 7 = 0 -7 -7 2y = -7 2 2

Y = - 4 ½ Day 5 Writing Linear Equations

To write the equation of a line in slope-intercept form, you need the slope and the y-intercept.

EX # 1 Write the equation of a line with slope = 2 that passes through the point (3,4).

We know that m = 2 and that the ordered pair gives us an x and a y value. (x, y)

y = mx + b * Substitute for the variables you know.

4 = 2(3) + b * Solve for b 4 = 6 + b -6 -6 -2 = b * Use the b value and the m value to write a new equation.

y = 2x -2

EX # 2 Write the equation of the line that passes through the points (1, 3) and (-3,-5).

First find m using the formula: m = y2 – y1 = -5 – 3 = -8 = 2 = 2 x2 – x1 -3 – 1 -4 1

Next pick one of the 2 ordered pairs to use for x and y. (1,3)

Substitute and solve for b. y = mx + b 3 = 2(1) + b 3 = 2 + b -2 -2 1 = b

Finally write a new equation y = 2x + 1 Day 6 Parallel and Perpendicular Lines

Parallel lines - Two lines in the same plane that never cross. - They have the SAME SLOPE.

Perpendicular lines - Two lines in the same plane that intersect at a right angle. ( 90 ◦) - Their slopes are negative reciprocals.

Ex. If m = 2 then perpendicular m = -1/2 Ex. If m = -3/4 then perpendicular m = 4/3

Think : “ flip and change sign”.

EX # 1 Write the equation of a line that passes through the point ( -2, 5) that is parallel to the line y = -4x + 2.

 Since the lines are parallel, they must have the same slopes.  The slope of y = -4x + 2 is -4.  Use m = -4 and ( -2, 5) y = mx + b 5 = -4(-2) + b 5 = 8 + b -8 -8 -3 = b  Write the new equation y = - 4x – 3

Ex # 2 Write the equation of the line passing through the point (3, -3) that is perpendicular to the line y = ¾ x + 5.

Since m = ¾ then perpendicular m = -4/3.

y = mx + b -3 = -4/3 (3) + b -3 = -4 + b +4 +4 1 = b Write the new equation y = -4/3 x + 1