Exploring Linear Equations through Tables, Graphs, and Equations

The video tutorial covers linear equations, focusing on identifying linear functions from tables, writing equations in slope-intercept form, and solving for slope and y-intercept using given points. It provides examples and exercises to reinforce understanding, with questions for students to complete after the video.

What is a key characteristic of a linear equation when viewed on a graph?

• It forms a curved line

• It forms a circle

• It forms a straight line

• It forms a zigzag pattern

How is the slope of a linear equation determined from a table?

• By dividing the change in Y by the change in X

• By subtracting the X values

• By adding the Y values

• By multiplying the X values

How do you verify if a function is linear from a table?

• Ensure the ratio of change in Y to change in X is constant

• Check if the product of X and Y is constant

• Sum the X values and compare to Y values

• Ensure the X values are all positive

What indicates a non-linear function based on changes in Y?

• Constant change in Y

• Inconsistent change in Y

• Zero change in Y

• Linear change in Y

What formula is used to find the slope in slope-intercept form?

• y2 + y1 / x2 + x1

• y2 - y1 / x2 - x1

• x2 - x1 / y2 - y1

• x2 + x1 / y2 + y1

What does the y-intercept represent in the equation of a line?

• The Y value when X is zero

• The minimum X value

• The X value when Y is zero

• The maximum Y value

How do you determine the y-intercept if it's not directly given in the table?

• By setting Y to zero and solving for X

• By extrapolating the line on the graph

• By setting X to zero and solving for Y

• By using the slope to calculate from a known point

What is the correct slope-intercept form of an equation?

• x = my + b

• x = by + m

• y = bx + m

• y = mx + b

If given two points, how can you find the slope?

• Subtract the Y values and divide by the difference in X values

• Add the Y values and divide by the sum of X values

• Multiply the X values and divide by the product of Y values

• Divide the sum of Y values by the difference in X values

What is the next step after finding the slope and y-intercept?

• Write the equation in slope-intercept form

• Determine the length of the line

• Calculate the area under the curve

• Plot the points on a graph