Exploring Linear Equations

This video tutorial covers writing linear equations using intercept form, focusing on finding the slope and y-intercept. It demonstrates how to write equations from graphs, tables, and real-world situations. The tutorial includes examples and encourages viewers to practice by pausing the video. Key concepts include understanding slope as the rate of change and the y-intercept as the starting value. The video concludes with a real-world example of cooling coffee, reinforcing the application of linear equations.

What is the first step in writing a linear equation in intercept form?

• Graph the equation

• Substitute values into the equation

• Find the slope or rate of change

• Find the y-intercept

What is the slope of a line that decreases from left to right with a rise of 3 and a run of 1?

• 3

• -3

• 1

• -1

If a horizontal line crosses the y-axis at -5, what is the equation of the line?

• y = 0x - 5

• y = -5x

• y = 5

• y = -5

In a real-world situation, what does the y-intercept represent?

• The total cost

• The slope

• The initial value or starting point

• The rate of change

Josie pays a fee of $2 to use a basket and $3 per pound of produce. What is the equation representing this situation?

• y = 3x + 2

• y = 3x - 2

• y = 2x + 3

• y = 2x - 3

What formula is used to find the slope from a table of values?

• y2 / y1 over x2 / x1

• y2 * y1 over x2 * x1

• y2 - y1 over x2 - x1

• y2 + y1 over x2 + x1

Given the points (0, -12) and (6, -11), what is the slope?

• 1/6

• -1/6

• -6

• 6

If Shelby's painting rate is 15 square feet per minute and she starts with 24 square feet painted, what is the equation?

• y = 15x + 24

• y = 24x + 15

• y = 24x - 15

• y = 15x - 24

Summer's coffee cools at a rate of 0.5 degrees per minute from an initial temperature of 120 degrees. What is the equation?

• y = 0.5x + 120

• y = -0.5x + 120

• y = 0.5x - 120

• y = -0.5x - 120

What is the y-intercept in the equation y = -0.5x + 120?

• -120

• 120

• -0.5

• 0.5