Understanding the Equation of a Straight Line

The video tutorial explains how to determine the equation of a straight line by identifying its slope and y-intercept. It begins with an introduction to the basic form of a line equation, y = ax + b, where 'a' is the slope and 'b' is the y-intercept. The tutorial then guides viewers through the process of calculating the slope using two points on the line and finding the y-intercept algebraically. Finally, it demonstrates how to write the complete equation of the line using the calculated slope and y-intercept.

What is the basic form of the equation of a straight line?

• y = ax + b

• y = a + bx

• x = a + by

• x = ay + b

What do the variables 'a' and 'b' represent in the line equation y = ax + b?

• a is the x-intercept, b is the slope

• a is the slope, b is the x-intercept

• a is the slope, b is the y-intercept

• a is the y-intercept, b is the slope

How do you calculate the slope 'a' using two points (x1, y1) and (x2, y2)?

• (y1 - y2) / (x1 - x2)

• (y2 - y1) / (x2 - x1)

• (x2 - x1) / (y2 - y1)

• (x1 - x2) / (y1 - y2)

What is the slope of the line if the points are (1, 4) and (3, 7)?

• 1.5

• 2

• 3

• 0.5

Why can't we assume the y-intercept when the line doesn't cross perfectly on the y-axis?

• Because it might be a decimal value

• Because it is always a whole number

• Because it is always negative

• Because it is always zero

What is the algebraic method used to find the y-intercept 'b'?

• Substitute known values into y = ax + b

• Use the quadratic formula

• Use the distance formula

• Use the midpoint formula

If the slope 'a' is 1.5 and a point on the line is (1, 4), what is the y-intercept 'b'?

• 4.5

• 1.5

• 3.5

• 2.5

What is the final equation of the line with slope 1.5 and y-intercept 2.5?

• y = 1.5x + 2.5

• y = 2.5x + 1.5

• y = 1.5x - 2.5

• y = 2.5x - 1.5

Which of the following is NOT a step in finding the equation of a line?

• Substituting known values

• Identifying the y-intercept

• Calculating the slope

• Finding the midpoint

Why is it important to use ordered pairs consistently when solving for 'b'?

• To ensure the slope is zero

• To avoid calculation errors

• To make the equation more complex

• To make the y-intercept negative