8 mistakes learners make with the equation of a straight line, each one named and explained.
In y = mx + c the m is the gradient and the c is where it crosses the y-axis.
A line through (2, 5) is given the equation y = 2x + 5, taking the 5 straight from the point.
The point contains a number that looks exactly like a c, and using it saves a step.
Question. Through (2, 5) and (6, 13)
A common answer. y = 2x + 5
The answer. y = 2x + 1
Why. The point (2, 5) is not on the y-axis, so its y-coordinate is not the intercept.
Only a point with x = 0 gives the intercept directly. Otherwise you have to solve for it.
2y = 6x + 8 is rewritten as y = 6x + 8, or as y = 3x + 8.
Dividing the term you are focused on is the step you remember; the others are easy to leave.
Question. 2y = 6x + 8
A common answer. y = 3x + 8
The answer. y = 3x + 4
Why. Everything on the right has to be divided by 2, not just the x term.
Whatever you do to one term you do to every term. Check each one before moving on.
A line with gradient 2 through (0, -5) is written as y = -5x + 2.
Both numbers are known and y = mx + c does not say aloud which slot each belongs in.
Question. Gradient 2, through (0, -5)
A common answer. y = -5x + 2
The answer. y = 2x - 5
Why. The gradient multiplies the x, so the 2 goes with the x.
Write y = mx + c above your answer and match the letters across. The slots then cannot swap.
The y-intercept of y = -2x + 6 is given as (6, 0).
The number 6 is right and only its position in the bracket is wrong.
Question. y = -2x + 6
A common answer. (6, 0)
The answer. (0, 6)
Why. The y-intercept sits on the y-axis, where x is zero.
On the y-axis, x is always 0. The zero goes first.
For y = 4x - 7 the gradient is given as -7 or 7.
Both numbers are in the equation and nothing on the page labels which is which.
Question. y = 4x - 7
A common answer. the gradient is -7
The answer. the gradient is 4
Why. The gradient is the number attached to x, because it is what multiplies the steepness.
The gradient always travels with an x. If your answer has no x beside it, it is the intercept.
The gradient of y = 4x - 7 is given as -4.
There is a minus sign in the equation, and it is easy to attach it to the wrong number.
Question. y = 4x - 7
A common answer. the gradient is -4
The answer. the gradient is 4
Why. The minus belongs to the 7, not to the 4.
The sign in front of the x is the gradient's sign. Nothing else affects it.
A line through (0, -5) is written with + 5 at the end.
Copying a negative number into an equation that already has a plus sign in the template.
Question. Through (0, -5) with gradient 2
A common answer. y = 2x + 5
The answer. y = 2x - 5
Why. The line crosses the y-axis below the origin, so the constant is negative.
Substitute x = 0 into your finished equation. It should give the point you were told.
Asked where a line crosses the x-axis, the y-intercept is given instead.
The y-intercept is the crossing point practised most often, so it is the one that surfaces.
Question. Where y = 3x - 4 crosses the x-axis
A common answer. (0, -4)
The answer. (4/3, 0)
Why. On the x-axis the y-coordinate is zero, so you set y to 0 and solve.
Set the other variable to zero. The axis you are crossing is the one you keep.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.