Question

A student writes the equation for a line that has a slope

Answer 1

Answer: the student is incorrect.

Point slope form: y - y1 = m (x - x1)
Used when given one point and a slope (m)

(2, -8) and a slope of -6
y - y1 = m (x - x1)
y - (-8) = -6(x - 2)
y + 8 = -6x + 12
- 8 - 8
y = -6x + 4

Check your answer using (2, -8):
y = -6x + 4
-8 = -6(2) + 4
-8 = -12 + 4
- 8 = -8
This statement is true.


Another way to explain why they are incorrect:
y - (-8) = -6(x - 2)
y + 8 = -6x + 12 (This is where they went wrong. Two negatives next to each other when subtracting, make a positive)
y + 8 = -6x + 12
- 8 - 8
y = -6x + 4


Hope this helps!

Answer 2

Y = mx + c
Where
y is the y of (2, -8)
x is the x of (2, -8)
m is the gradient or slope
c is the y intercept (you don’t know what it is)

Put into equation and find c

Once find c rewrite the equation with only the m and c in numbers

Eg

y = 5x + 3 (this is an example not the answer)

Hope this is helpful if you don’t understand please comment