Finding Slopes and Parallel Lines

The video tutorial explains how to find a line parallel to a given line that passes through a specific point. It starts by identifying the slope of the given line by rearranging it into the slope-intercept form. Then, it uses the slope to set up the equation of the parallel line. Finally, it calculates the y-intercept by substituting the given point into the equation, resulting in the final equation of the parallel line.

What is the initial equation given in the problem?

• 3x + 2y = 6

• 2x + 3y = 6

• 3x - 2y = 6

• 2x - 3y = 6

What is the key characteristic of parallel lines?

• They intersect at one point.

• They are perpendicular.

• They have the same y-intercept.

• They have the same slope.

Why do parallel lines not intersect?

• They are perpendicular.

• They have the same slope.

• They have the same y-intercept.

• They have different slopes.

What is the first step to find the slope of the given line?

• Divide both sides by 2.

• Multiply both sides by 2.

• Subtract 3x from both sides.

• Add 3x to both sides.

What is the slope of the line after rearranging the equation?

• -2/3

• -3/2

• 3/2

• 2/3

What is the next step after finding the slope to determine the parallel line?

• Find the x-intercept by substituting the given point.

• Find the y-intercept by substituting the given point.

• Multiply the slope by the x-coordinate.

• Divide the slope by the y-coordinate.

What point is given to find the parallel line?

• (4, 1)

• (-4, 1)

• (-4, -1)

• (4, -1)

What is the value of 3/2 times 4?

• 2

• 4

• 6

• 8

What is the y-intercept (b) of the parallel line?

• 7

• -6

• -7

• 6

What is the final equation of the parallel line?

• y = -3/2x - 7

• y = 3/2x - 7

• y = -3/2x + 7

• y = 3/2x + 7