Write Linear Equations from Point and Slope

This video tutorial explains how to write the equation of a line given a point and a slope. It introduces the slope-intercept form, y = mx + b, and demonstrates how to determine the y-intercept using two examples. The first example uses a slope of 3 and a point to find the y-intercept, resulting in the equation y = 3x + 18. The second example uses a slope of 5/3 and a different point, leading to the equation y = 5/3x - 17. The video emphasizes understanding the relationship between the slope, y-intercept, and the line's equation.

What does the 'm' in the equation y = mx + b represent?

• Slope of the line

• x-intercept

• Maximum value of y

• y-intercept

Where does the line cross the y-axis in the equation y = mx + b?

• At the point (0, b)

• At the point (b, 0)

• At the point (0, m)

• At the point (m, 0)

What is the correct way to write an equation given a slope and a point on the line?

• y = mx + c, where m is the slope and c is calculated based on the point

• y = mx, ignoring the point

• y = b, where b is the y-coordinate of the point

• x = my + b, where m is the slope

What does the equation y = mx + b typically represent?

• A polynomial

• A linear equation

• An exponential function

• A quadratic function

If the slope (m) is 3, what is the initial form of the equation?

• y = 3 + x

• y = 3x

• y = x + 3

• y = x/3

How do you determine the y-intercept when you have a point and a slope?

• Substitute the x-value of the point into the equation

• Adjust the slope until the line fits the point

• Substitute the y-value of the point into the equation

• Use the slope to calculate the change in y

What is the y-intercept in the equation y = 3x + 18?

• 3

• 18

• x

• y

In the equation y = 5/3x - 17, what does the number -17 represent?

• Maximum value of y

• y-intercept

• x-intercept

• Slope of the line

What must be added to 10 to get -7 in the context of the equation y = 5/3x + b?

• 17

• -17

• 3

• -3

If a line has a slope of 5/3 and passes through the point (6, -7), what is the equation of the line?

• y = 3/5x + 6

• y = 3/5x - 7

• y = 5/3x - 17

• y = 5/3x + 17