Question

solve for y = -x + 2 and y = x - 6 Each line must: 1- Be labeled 2- Formed by three points, one of which is the y-intercept. 3- Extended with arrows.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for y = -x + 2 and y = x - 6, we can start by finding the y-intercepts and plotting three points for each line.

1) Line y = -x + 2:
To find the y-intercept, set x = 0:
y = -0 + 2
y = 2
So the y-intercept is (0, 2).

Now pick two additional x-values to find the corresponding y-values and plot those points:
Let x = 1:
y = -(1) + 2
y = -1 + 2
y = 1
So another point on the line is (1, 1).

Let x = -1:
y = -(-1) + 2
y = 1 + 2
y = 3
Thus, another point on the line is (-1, 3).

Plot the points (0, 2), (1, 1), and (-1, 3) on the coordinate plane. Draw a line passing through these points and extend it with arrows on both ends. Label it "y = -x + 2".

2) Line y = x - 6:
To find the y-intercept, set x = 0:
y = 0 - 6
y = -6
So the y-intercept is (0, -6).

Now pick two additional x-values to find the corresponding y-values and plot those points:
Let x = 1:
y = (1) - 6
y = -5
So another point on the line is (1, -5).

Let x = -1:
y = (-1) - 6
y = -7
Thus, another point on the line is (-1, -7).

Plot the points (0, -6), (1, -5), and (-1, -7) on the coordinate plane. Draw a line passing through these points and extend it with arrows on both ends. Label it "y = x - 6".

Here is a visual representation of the lines: