Understanding Standard Form of Linear Equations

This video tutorial covers writing equations in standard form, defined as Ax + By = C, where A, B, and C are integers and A is positive. The lesson includes examples of equations in standard form and those that are not, and demonstrates how to transform equations from slope-intercept and point-slope forms into standard form. The tutorial also provides practice problems for converting equations to standard form, emphasizing the importance of integer coefficients and a positive leading coefficient.

What is the standard form of a linear equation?

• y = a(x - h)^2 + k, where (h, k) is the vertex

• ax^2 + bx + c = 0, where a, b, and c are constants

• y = mx + b, where m is the slope and b is the y-intercept

• ax + by = c, where a, b, and c are integers and a is positive

Why is the equation 3.2x + 4.2y = 7.3 not in standard form?

• The equation is not in slope-intercept form

• The equation is not linear

• The equation does not have a y-intercept

• The coefficients are not integers

Which of the following is a correct step in converting y = 2/5x + 7 to standard form?

• Add 5 to both sides

• Multiply the entire equation by 5 to eliminate the fraction

• Subtract 7 from both sides

• Divide the entire equation by 2

What is the first step in converting an equation from point-slope form to standard form?

• Distribute the slope to both terms inside the parentheses

• Subtract the y-intercept from both sides

• Add the slope to both sides

• Multiply by the reciprocal of the slope

In the equation y - 2 = 1/4(x + 1), what is the slope?

• 1

• -1/4

• 2

• 1/4

What is the standard form of the equation y = -4x + 3?

• 4x + y = 3

• -4x + y = 3

• x - 4y = 3

• y = 4x - 3

If a line passes through the points (0, 3) and (2, -5), what is the slope?

• -1/2

• 1/2

• 4

• -4

Which of the following equations is in standard form?

• 3x + 4y = 12

• y = 3x + 4

• y = 4x - 3

• x^2 + y^2 = 25

What is the result of multiplying the equation -2x + y = 5 by -1?

• -2x - y = -5

• 2x + y = 5

• -2x + y = 5

• 2x - y = -5

How do you determine the x-intercept from an equation in standard form?

• Set y to zero and solve for x

• Use the quadratic formula

• Set x to zero and solve for y

• Find the slope and y-intercept