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

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Understand the Problem

The question is asking to identify the slope and y-intercept from the linear equation given in standard form, 3x + y = -7. To solve it, we need to convert the equation to slope-intercept form (y = mx + b) and extract the values for m (slope) and b (y-intercept).

Answer

$m = -3$, $b = -7$
Answer for screen readers

The slope is $m = -3$ and the y-intercept is $b = -7$.

Steps to Solve

  1. Convert to Slope-Intercept Form

Transform the standard form equation $3x + y = -7$ to slope-intercept form, which is $y = mx + b$.

Start by isolating $y$: $$ y = -3x - 7 $$

  1. Identify the Slope (m)

From the equation $y = -3x - 7$, the coefficient of $x$ represents the slope $m$.

Thus, $$ m = -3 $$

  1. Identify the Y-Intercept (b)

In the equation $y = -3x - 7$, the constant term is the y-intercept $b$.

So, $$ b = -7 $$

The slope is $m = -3$ and the y-intercept is $b = -7$.

More Information

The slope indicates that for every 1 unit increase in $x$, $y$ decreases by 3 units. The y-intercept means the line crosses the y-axis at -7.

Tips

  • Forgetting to isolate $y$ properly when converting to slope-intercept form.
  • Misidentifying the slope as the y-intercept or vice versa.
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