An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 10 right parenthesis and left parenthesis 1 comma negative 7 right parenthesis.

Question

Is this the correct graph of 3x−y=10?

(1 point)

Answer 1

To determine if the upward slanting line graphed on the coordinate plane represents the equation \(3x - y = 10\), we should first rearrange the equation into slope-intercept form (y = mx + b) to identify its slope and y-intercept.

Starting from the given equation:

\[ 3x - y = 10 \]

we can rearrange it:

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

Multiplying through by -1 gives us:

\[ y = 3x - 10 \]

Now, we can identify the slope (m) and y-intercept (b):

• Slope (m) = 3
• Y-intercept (b) = -10

The y-intercept indicates that the line crosses the y-axis at (0, -10), which matches the point you've given.

Next, we can find another point on the line to verify if it is consistent with the point (1, -7).

Plugging \(x = 1\) into the equation:

\[ y = 3(1) - 10 = 3 - 10 = -7 \]

This confirms the point (1, -7) is also on the line.

Since the line you described passes through both (0, -10) and (1, -7), and corresponds with the equation \(3x - y = 10\), we conclude that this is indeed the correct graph.