Given 3x + y = -7, identify the slope and y-intercept.

Understand the Problem

The question is asking to find the slope (m) and the y-intercept (b) of the equation 3x + y = -7 by rewriting it in slope-intercept form (y = mx + b).

Answer

m = $-3$, b = $-7$

Steps to Solve

Rearranging the equation to isolate y

Starting with the equation:

$$ 3x + y = -7 $$

We want to isolate ( y ) on one side of the equation. To do this, subtract ( 3x ) from both sides:

$$ y = -3x - 7 $$

Identifying the slope (m)

Now that we have the equation in slope-intercept form ( y = mx + b ), we can identify the slope. Here, the slope ( m ) corresponds to the coefficient of ( x ):

$$ m = -3 $$

Identifying the y-intercept (b)

Next, we look for the y-intercept, which corresponds to the constant term in the equation. From our rearranged equation:

$$ b = -7 $$

The slope ( m ) is ( -3 ) and the y-intercept ( b ) is ( -7 ).

More Information

In the slope-intercept form ( y = mx + b ), the slope represents the rate of change of ( y ) with respect to ( x ), while the y-intercept indicates the point where the line crosses the y-axis.

Tips

Not isolating ( y ) correctly: Make sure to perform the same operation on both sides of the equation.
Misidentifying coefficients: Double-check that you're correctly identifying the slope and y-intercept from the final equation.

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