Understanding Linear Equations and Slope

This lesson focuses on understanding the slope of a line in the context of the equation y=mx+b. It covers graphing linear equations using a T-chart, plotting ordered pairs, and calculating the slope from a graph. The lesson emphasizes the connection between the slope and the coefficient of x in the equation. Practice problems and homework help are provided to reinforce these concepts.

What is the general form of a linear equation?

• y = ax + b/x

• y = a/x + b

• y = ax^2 + bx + c

• y = mx + b

When graphing the equation y = 2x + 3, what is the y-intercept?

• 5

• 0

• 3

• 2

How do you calculate the slope of a line given two points?

• Subtract the x-coordinates from the y-coordinates

• Multiply the x-coordinates by the y-coordinates

• Add the x-coordinates and y-coordinates

• Divide the difference in y-coordinates by the difference in x-coordinates

What is the slope of the line represented by the equation y = -3x + 2?

• 3

• -2

• 2

• -3

Which of the following equations is in the form y = mx + b?

• y = 4x - 5

• 2x + 3y = 6

• x^2 + y = 1

• y/x = 2

If an equation is not in the form y = mx + b, what should you do first?

• Solve for y

• Multiply by x

• Add 1 to both sides

• Divide by x

What is the slope of the line y = 5x - 4?

• 5

• 1

• -4

• 0

In the equation y = mx + b, what does 'b' represent?

• The coefficient of x

• The x-intercept

• The y-intercept

• The slope

What happens to the graph of a line if the slope is negative?

• It becomes a vertical line

• It slopes downwards from left to right

• It becomes a horizontal line

• It slopes upwards from left to right

Which point does the line y = 2x + 3 cross the y-axis?

• (0, 3)

• (2, 0)

• (0, 2)

• (3, 0)