Question

Which graph shows the correct solution for y=-3 x-y=8

Answer 1

"Third graph" in the attached picture.

Explanation:

The correct graph would be the "intersection" of the lines:

y = -3, and

x - y = 8

We know, y = -3 is a horizontal line at y = -3 and the next is a line. By looking at the first equation, we can eliminate 2 graphs and thus find the correct graph.

y = -3 is a horizontal line at y = -3, the first graph has the line y = 3, so we can eliminate this even without looking at the graph of 2nd equation.

The second graph has a vertical line, no horizontal, so we can eliminate this choice as well.

The third graph has y = -3 (horizontal line at y = -3) and thus this is the correct choice. Also, x - y = 8 means y = x -8, which is the other graph shown.

correct answer is the "third graph".

Answer 2

Answer: last option.

Explanation:

The equation of the line in slope-intercept form is:

`y=mx+b`

Where m is the slope and b the intersection with the y-axis.

The line
`y=-3` is a line with slope 0 that cut the y-axis at (0,-3)

Solve for y from the second equation:

`x-y=8\\x-8=y`

The line
`y=x-8` is a line with slope 1 that cut the y-axis at (0,-8)

You can identify these lines in the last graph, where the point of intersection between them is the solution of the system of equations.