Understanding Linear Equations

The video tutorial explains how to write the equation of a line in slope-intercept form. It begins by introducing the formula y = mx + b, where m is the slope and b is the y-intercept. The tutorial uses a given slope of 1/3 and a point (-12, -14/3) to demonstrate how to solve for the y-intercept. By substituting the point into the equation, the tutorial shows the step-by-step process of calculating b, resulting in the final line equation y = 1/3x - 2/3.

What is the first step in writing the equation of a line when given a slope and a point?

• Use the standard form

• Identify the y-intercept

• Use the point-slope form

• Identify the slope

In the slope-intercept form of a line, what does the 'm' represent?

• The x-coordinate

• The slope

• The y-intercept

• The y-coordinate

What is the equation of a line in slope-intercept form?

• b = mx + y

• x = my + b

• y = mx + b

• y = b + mx

How do you find the y-intercept when given a point and a slope?

• Divide the y-coordinate by the slope

• Multiply the slope by the x-coordinate

• Add the slope to the y-coordinate

• Substitute the point into the equation and solve for b

What is the result of multiplying the slope 1/3 by the x-coordinate -12?

• 4

• 12

• -12

• -4

What operation is performed to isolate b on the right-hand side of the equation?

• Subtract 4 from both sides

• Divide both sides by 3

• Multiply both sides by 3

• Add 4 to both sides

What is the common denominator used to combine 4 and -14/3?

• 4

• 12

• 2

• 3

What is the y-intercept of the line after solving the equation?

• 2/3

• -1/3

• -2/3

• 1/3

What is the final equation of the line?

• y = -1/3x + 2/3

• y = -1/3x - 2/3

• y = 1/3x + 2/3

• y = 1/3x - 2/3

What is the significance of the y-intercept in the equation of a line?

• It determines the slope of the line

• It is the point where the line crosses the x-axis

• It is the point where the line crosses the y-axis

• It determines the direction of the line