Equation of Lines

Concept:

In geometry, a line is uniquely defined by two points. In algebra, a line is uniquely defined by a first-degree equation. The equation may be written in different forms, including the point-slope form y – y₁ = m(x – x₁), the slope-intercept form y = mx + b, and the general form Ax + By = C, each of which is useful in different contexts. There is still a requirement of two pieces of information, but this information is appears in the equation as parameter values. Changing the line means changing the parameters of the equation.

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS

1. Which of the following axis of rotation would yield a representative cross-section of the solid as a disk?

X-axis Y-axis Both a and b None of the above

Equation of Lines

Concept:

Points form:

P = ( x₁ , y₁ ) Q = ( x₂ , y₂ )

Ax + By = C

y = mx + b

y – y₁ = m(x – x₁)

y = k

x = h

Parent Function

Parent Function

Modified Function

Horizontal Stretch/Shrink

Vertical Stretch/Shrink

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS

Concept:

Points form:

P = ( x1 , y1 ) Q = ( x2 , y2 )

Ax + By = C

y = mx + b

y – y1 = m(x – x1)

y = k

x = h

Parent Function

Parent Function

Modified Function

Horizontal Stretch/Shrink

Vertical Stretch/Shrink

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS

P = ( x₁ , y₁ ) Q = ( x₂ , y₂ )

y – y₁ = m(x – x₁)