Question

14.

1. $4y - 8 = 2x$
2. $y - 3x = -15$

15.

1. $-2y + x = 2y - 8$
2. $2x + y = 10x - 1$

Explanation:

Since the problem is not clearly stated (it just shows some equations and graphs without a specific question like solving for \(x\), \(y\), finding the slope, or determining if the lines are parallel/perpendicular, etc.), I'll assume a common task like converting the linear equations to slope - intercept form (\(y = mx + b\)) for one of the equations, say equation 17: \(4y-8 = 2x\).

Step 1: Isolate the \(y\) - term

We start with the equation \(4y-8 = 2x\). First, we add 8 to both sides of the equation to get the \(y\) - term by itself.
\(4y-8 + 8=2x + 8\)
\(4y=2x + 8\)

Step 2: Solve for \(y\)

Now, we divide every term in the equation by 4 to solve for \(y\).
\(y=\frac{2x + 8}{4}\)
We can simplify this fraction. We know that \(\frac{2x}{4}=\frac{1}{2}x\) and \(\frac{8}{4} = 2\). So, \(y=\frac{1}{2}x+2\)

If you want to solve a different equation or perform a different operation (like finding the intersection of lines, determining the slope from the graph, etc.), please provide more details about what you want to do with these equations and graphs.

Answer:

Step 1: Isolate the \(y\) - term

We start with the equation \(4y-8 = 2x\). First, we add 8 to both sides of the equation to get the \(y\) - term by itself.
\(4y-8 + 8=2x + 8\)
\(4y=2x + 8\)

Step 2: Solve for \(y\)

Now, we divide every term in the equation by 4 to solve for \(y\).
\(y=\frac{2x + 8}{4}\)
We can simplify this fraction. We know that \(\frac{2x}{4}=\frac{1}{2}x\) and \(\frac{8}{4} = 2\). So, \(y=\frac{1}{2}x+2\)

If you want to solve a different equation or perform a different operation (like finding the intersection of lines, determining the slope from the graph, etc.), please provide more details about what you want to do with these equations and graphs.