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

Reposition the line in the coordinate system by dragging the points on the line or by dragging the line itself. The coefficients of the equations will change to match the line as currently plotted. You may also reposition the line by typing new coordinates for either or both of the points, or by typing the coefficients of any one of the equations at a time. The line will reposition, and the other equations will be updated, after you press the Enter key.

EXPLORATIONS

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)