Exploring Linear Equations in Standard Form

The video tutorial introduces the concept of linear equations in standard form using a fairytale theme. It explains how to plot a line between two points, Princess Eudora and Prince Charming, and convert the equation into standard form. The tutorial also covers calculating the slope of a line using the standard form equation, demonstrated through the prince's escape path. The video concludes with a whimsical note on the prince's fairytale ending.

What is the standard form of a linear equation?

• y = mx + b

• ax + by = c

• a^2 + b^2 = c^2

• x^2 + y^2 = r^2

In the standard form equation ax + by = c, which of the following statements is true?

• a and b can both be zero

• a and b cannot both be zero

• a, b, and c must all be positive

• c must always be zero

If Princess Eudora is at point (8, 0) and Prince Charming is at (0, 2), what is the equation of the line in standard form?

• x - 4y = 8

• 4x + y = 8

• 4x - y = 8

• x + 4y = 8

What is the first step to convert a linear equation from slope-intercept form to standard form?

• Multiply both sides by the slope

• Add the y-intercept to both sides

• Rearrange the equation to isolate y

• Substitute the slope and y-intercept into the equation

What is the slope of the line passing through points (8, 0) and (0, 2)?

• 2

• -2

• 1/4

• -1/4

How do you rearrange the equation y = mx + b into standard form?

• Add mx to both sides and then multiply by a constant

• Subtract mx from both sides and then multiply by b

• Add mx to both sides and then multiply by b

• Subtract mx from both sides and then multiply by a constant

What is the equation of the line along which Prince Charming runs for the door?

• y - 3x = 2

• 3x - y = 2

• y + 3x = 2

• 3x + y = 2

What is the slope of the line y - 3x = 2?

• -1/3

• 1/3

• 3

• -3

How do you find the slope from the standard form of a linear equation?

• Divide b by a

• Negative b over a

• Divide a by b

• Negative a over b

If a is -3 and b is 1 in the standard form equation, what is the slope?

• 1/3

• -1/3

• 3

• -3