Linear Equation Forms

Linear Equation Forms

The equation of a line is called a linear equation.

There are multiple forms which a linear equation can be written.

It is recommended that you take notes from the slides which follow.

Multiple Choice

The equation of a line is called:

• an algebraic equation

• a quadratic equation

• a linear equation

Linear Equation Forms (take notes)

The 3 common linear equation forms are:

1) slope-intercept form

2) point-slope form

3) standard form

Other forms include general form and intercept form.

Multiple Select

Select the 3 common linear equation forms mentioned on the previous slide:

• standard form

• quadratic form

• slope-intercept form

• point-slope form

• algebraic form

Slope-intercept Form

A linear equation is in slope-intercept form when that equation is solved for y such that:

y = mx + b

where y is the output variable, x is the input variable, m is the slope of the line, and (0,b) is the y-intercept of the line.

Multiple Choice

The slope of the line represented by the equation y=mx+b is:

• x

• y

• m

• b

Multiple Choice

The y-intercept of the line represented by y=mx+b is:

• (0, x)

• (0, y)

• (0, m)

• (0, b)

Point-slope Form

The point-slope form of a linear equation is:

y - y₁ = m ( x - x₁ )

where ( x₁ , y₁ ) is a point on the line and m is the slope of the line.

Multiple Choice

The slope of the line represented by the equation

y - y₁ = m ( x - x₁ ) is:

• x₁

• y₁

• m

• x

Multiple Choice

The point on the line represented by the equation

y - y₁ = m ( x - x₁ ) is:

• ( x, y)

• ( x₁ , y₁ )

• ( y, x)

• ( y₁ , x₁ )

Standard Form

The standard form of a linear equation is

ax + by = c

where x is the input variable, y is the output variable, and a, b, and c are constants (real numbers).

Multiple Choice

Which of the following linear equations is in standard form?

• y = 3x + 4

• y - 2 = 5 (x + 1)

• 4x + 5y = 60

• x = 3y + 4

Multiple Choice

Which of the following linear equations is in slope-intercept form?

• y = 3x + 4

• y - 2 = 6 ( x + 1)

• 4x + 5y = 60

• x = 3y + 4

Multiple Choice

Which of the following linear equations is in point-slope form?

• y = 3x + 4

• y - 5 = 2 ( x - 1)

• 4x + 5y = 60

• x = 3y + 4