Line equation, graph and transformation
Line equation
We know that the equation of a line is given by
y = mx + b, where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.
We want to find the equations for both lines:
Line A: y = mx + b
Line B: y = mx + b
y- intercept
We have that the interception of the line A with the y-axis is y = 3, then b = 3.
We have that the interception of the line B with the y-axis is y=-6, then b = -6.
Then, we have that:
Line A: y = mx + 3
Line B: y = mx - 6
m: slope
The slope is the number of unities that the line changes upward or downward for each unity of x from left to right.
We have that the line A goes 2 unities up on each unity of x from left to right. Then m = 2
The line B goes 2 unities down on each unity of x from left to right. Then m = -2
Then, we have that:
Line A: y = 2x + 3
Line B: y = -2x - 6
Answer A: y = 2x + 3
Answer B: y = -2x - 6
Transformation
In order to obtain line B from line A, we have to
1. substract 9 (9 unities of downward displacement):
Line A: y = 2x + 3
↓
y = 2x + 3 - 9
↓
y = 2x - 6
2. change the sign of x (reflection across y axis):
y = 2x - 6
↓
y = 2(-x) - 6
↓
Line B: y = -2x - 6