Question

Is this the correct graph of
?
(1 point)
3x − y = 10
Yes, it is the correct
graph because the
slope is 3 and the -
intercept is
.
y
(0, − 10)
Yes, it is the correct
graph because the
slope is and the
-intercept is
.
−3
y
(0, − 10)
No, it is not the
correct graph
because the slope is
and the -
intercept is
.
−3 y
(0, − 10)
No, it is not the
correct graph
because the slope is
3 and the -intercept
is .
y
(0, − 10)
P1 1 , -7
P2 0,-10

Answer 1

To determine whether the graph of the equation \(3x - y = 10\) is correct, we can rewrite the equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

1. Rewrite the equation in the form \(y = mx + b\):

\[
3x - y = 10
\]

Rearranging gives:

\[
-y = -3x + 10
\]

Multiplying everything by -1 yields:

\[
y = 3x - 10
\]

2. From this form, we can see:
- The slope \(m\) is \(3\).
- The y-intercept \(b\) is \(-10\) (the point where the line crosses the y-axis, which is \((0, -10)\)).

Now, let's evaluate the statements provided:

1. **Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).**

This statement is **correct**.

2. **Yes, it is the correct graph because the slope is -3 and the y-intercept is (0, -10).**

This statement is **incorrect** because the slope is \(3\), not \(-3\).

3. **No, it is not the correct graph because the slope is -3 and the y-intercept is (0, -10).**

This statement is also **incorrect** for the same reason; the slope is \(3\).

4. **No, it is not the correct graph because the slope is 3 and the y-intercept is (0, -10).**

This statement is **incorrect** as well because it is actually the correct graph.

So, the correct response is the first one: **Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).**