Answer:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
For the particular case of horizontal lines, those will be of the form:
y = constant.
The vertical lines will be of the form:
x = constant.
Let's start with line a, this is a vertical line, then will be:
x = constant.
To see the value of the constant, you need to see in which point it intersects the x-axis, in this case is in -4, then line a will be:
x = -4
For line b we have the same reasoning, in this case the line intersects the x-axis at x = 4, then line b is: x = 4.
Now for the horizontal lines:
Line c will be of the form:
y = constant
To find the value of the constant you need to see in which point the line intersects the y-axis.
In this case the line intersects the axis at y = 4.
Then this line can be written as: y = 4
For line d, we can see that it intersects the y-axis at -2, then this line will be written as:
y = -2.
For the case of line e we can use the first thing we wrote, let's find two points that belong to this line.
(0 , 1) and (4, -2)
Then the slope will be:
a = (-2 - 1)/(4 - 0) = -3/4
y = -(3/4)*x + b
To find the value of b, we can just replace the values of one of the points in the equation. I will use the point (0, 1), this means that we must replace x by 0, and y by 1.
1 = -(3/4)*0 + b
1 = b
Then the equation for line e is:
y = -(3/4)*x + 1.
