Reflection in the line x - 2 = 0, x = 2

k = 2

(-7, 8) → (2 x 2 - (-7), 8)

(-7, 8) → (4 + 7, 8)

(-7, 8) → (11, 8)

Note:
1. -- = + or -(-) = +
2. -(-7) = + 7

Gradient = $\frac{\mathrm{Change\; in\; Y}}{\mathrm{Change\; in\; X}}$ = $\frac{{\mathrm{Y}}_2-{\mathrm{Y}}_1}{{\mathrm{X}}_2-{\mathrm{X}}_1}$

Pick any two points from the table to calculate the gradient.

Using the first two points, (0, 1) and (2, 2).

Y₂ = 2
Y₁ = 1
X₂ = 2
X₁ = 0

Gradient = $\frac{\mathrm{2\; -\; 1}}{\mathrm{2\; -\; 0}}$ = $\frac{1}{2}$

Gradient = $\frac{\mathrm{Change\; in\; Y}}{\mathrm{Change\; in\; X}}$ = $\frac{{\mathrm{Y}}_2-{\mathrm{Y}}_1}{{\mathrm{X}}_2-{\mathrm{X}}_1}$

Pick any two points from the table to calculate the gradient.

Using the first two points, (0, 1) and (2, 2).

Y₂ = 2
Y₁ = 1
X₂ = 2
X₁ = 0

Gradient = $\frac{\mathrm{2\; -\; 1}}{\mathrm{2\; -\; 0}}$ = $\frac{1}{2}$

Using the first point (0, 1)

y - 1 = $\frac{1}{2}$(x - 0)

Get rid of the fraction by multiplying both sides by the denominator 2.

2 x y - 1 x 2 = 1(x - 0)

2y - 2 = x

2y = x + 2