Straight Lines: common misconceptions

If your child says… “Zero area means all the points are the same point.”

Ask together

Do the separate points spread away from their shared straight line?

What’s true

Separate points can enclose zero area when they lie along one straight line.

If your child says… “An upright line has zero slope.”

Ask together

What would you divide by when there is no horizontal change?

What’s true

An upright line has undefined slope because its horizontal change is zero.

If your child says… “For a right angle, I only change the slope’s sign.”

Ask together

In the centre, does changing only one-half’s sign give the falling line’s slope?

What’s true

A quarter-turn exchanges horizontal and vertical changes and reverses one sign.

If your child says… “An equation containing y describes an upright line.”

Ask together

Can you move upwards while keeping the same height?

What’s true

The equation names the fixed coordinate, while movement changes the other coordinate.

If your child says… “I must replace every x and y with the given coordinates.”

Ask together

How would an equation without variables describe the other points?

What’s true

The finished equation keeps variables so it describes every point along the line.

If your child says… “The x-intercept is the number added at the end.”

Ask together

At the x-axis crossing, what must y become?

What’s true

The added constant in slope-intercept form gives the y-axis crossing.

If your child says… “The gap between the y-axis crossings is the distance between the lines.”

Ask together

Which measured route is shorter: the vertical connector or the perpendicular connector?

What’s true

The vertical gap equals the shortest gap only when the parallel lines are horizontal.

If your child says… “The mirror image stops where the perpendicular reaches the mirror.”

Ask together

If the image stopped at H, would the mirror halve the joining segment?

What’s true

The image lies equally far beyond the mirror line along the perpendicular.