Rise Over Run Lesson

Slope-Intercept Form: y = mx + b

Point-Slope Form: y - y1 = m(x -x1)

Standard Form: Ax + By = C

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Parallel vs Perpendicular Lines

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Unit 3: Linear Functions

Slope or Rate of Change (symbol = m)

Rise Over Run

Slope Equation

Slope or Rate of Change (symbol = m)

Rise over Run

​Find the slope of this line

using rise over run.

Rise over Run

Slope Equation - Linear Regression

y1 ~ mx1+b

DESMOS

1. Add table

2. Input data

3. y1~mx1+b

Slope Equation - Linear Regression

y1 ~ mx1+b

DESMOS

1. Add table

2. Input data

3. y1~mx1+b

​rate of change (m) = 7

Slope Equation

​What is the slope of a line that passes through the points (5,-11) and (-9,17)?

HINT: Write the equation without the x1, y1, x2, and y2, then input coordinates or USE DESMOS.

DESMOS

1. Add table

2. Input data

3. y1~mx1+b

Slope Equation or

​What is the slope of a line that passes through the points (5,-11) and (-9,17)?

HINT: Write the equation without the x1, y1, x2, and y2, then input coordinates or USE DESMOS.

Answer = -2

DESMOS

1. Add table

2. Input data

3. y1~mx1+b

Multiple Choice

What is the slope of a line that passes through the points (26,7) and (-39,12)?

Use DESMOS to solve and SIMPLIFY!!!

• -1/13

• 5/13

• -13

• 13/5

y = mx+b

m = slope

b = y-intercept

Slope-Intercept Form

​Graph the line y = 3x - 2.

y = mx+b

m = slope

b = y-intercept

Slope-Intercept Form

​Graph the line y = 3x - 2.

(y - y1) = m(x-x1)

m = slope

(x1, y1) = given point on line

Point-Slope Form

​Given: point (3,-2), m = 1/2

Find the equation of a line in point-slope form.

HINT: Write the formula first without the x1 and y1, then input the coordinates.

(y - y1) = m(x-x1)

m = slope

(x1, y1) = given point on line

Point-Slope Form

(y - y1) = m(x-x1)

m = slope

(x1, y1) = given point on line

Point-Slope Form

​Which equation is best represented by the graph?

A) y + 2 = 7/5 (x+7)

B) y - 2 = 7/5 (x-7)

C) y + 2 = 5/7 (x+7)

D) y - 2 = 5/7 (x-7

(y - y1) = m(x-x1)

m = slope

(x1, y1) = given point on line

Point-Slope Form

​Which equation is best represented by the graph?

A) y + 2 = 7/5 (x+7)

B) y - 2 = 7/5 (x-7)

C) y + 2 = 5/7 (x+7)

D) y - 2 = 5/7 (x-7) - ANSWER

Multiple Choice

The graph of the linear function is shows on the grid.

Which equation is best represented by the graph?

• y + 7 = -3(x-4)

• y + 1 = -3(x+2)

• y - 4 = 3(x+7)

• y - 2 = 3(x-1)

Multiple Choice

Convert 2x - 5y = 10 into slope intercept form (y=mx+b)

• y = 2x - 2

• y = 2/5x - 2

  or

  $$y\ =\ \frac{2}{5}x-2$$

• y = -2x - 2

• y = -2/5x - 2

  or

  $$y\ =\ -\frac{2}{5}x-2$$

Parallel vs. Perpendicular

Parallel Lines

Perpendicular Lines

• lines with the same slope

.

y = 2/3x + 5

y = 2/3x - 7

• lines with opposite reciprocals for slope

• lines that intersect at a right angle

  .

y = 1/4x + 1

y = -4x + 6

Multiple Choice

What is the equation of a line in slope-intercept form that passes through the point (5,0) and is parallel to the line represented by y = 1.2x + 3.8

• y = 1.2x - 6

• y = -1.2x + 6

• y = 1.2x + 5

• y = -1.2x - 5

Multiple Choice

What is the equation of a line in slope-intercept form that passes through the point (2,-2) and is perpendicular to the line represented by y = 2/5x + 2?

• y = 5/2x - 7

• y = 5/2x + 7

• y = -5/2x - 3

• y = -5/2x + 3

Inequalities

Inequalities

Inequalities