Understanding Linear Equations

This video tutorial covers the general form of a linear equation, explaining how to convert it to slope-intercept form. It demonstrates finding vertical and horizontal intercepts and graphing the line using these intercepts and the slope. The tutorial also discusses finding additional points on the line and interpreting the slope in different ways to ensure accurate graphing.

What is the general form of a linear equation?

• y = mx + b

• x = my + b

• ax - by = c

• ax + by = c

How do you convert a linear equation from general form to slope-intercept form?

• Solve for x

• Solve for y

• Add a constant to both sides

• Multiply both sides by a constant

What is the slope of the equation y = -3x + 8?

• -8

• 3

• 8

• -3

What is the y-intercept of the equation y = -3x + 8?

• (0, -3)

• (0, 8)

• (8, 0)

• (-3, 0)

How do you find the vertical intercept using the general form of the equation?

• Set y to 0 and solve for x

• Subtract x from y

• Set x to 0 and solve for y

• Add x and y

What is the horizontal intercept of the equation 3x + 2y = 16?

• (0, 16/3)

• (0, 8)

• (16/3, 0)

• (8, 0)

Which point is used as a starting point for graphing the line?

• Any random point

• Horizontal intercept

• Vertical intercept

• Origin

How do you determine additional points on the line using the slope?

• Go up and left

• Go up and right

• Go down and left

• Go down and right

What happens if you interpret the slope as positive 3 over negative 2?

• You go up and left

• You go up and right

• You go down and left

• You go down and right

Why is it sometimes better to interpret the slope as -3 over positive 2?

• It changes the y-intercept

• It changes the x-intercept

• It makes calculations easier

• It keeps the graph on the coordinate plane