Questions: Graph the equation by finding the slope and y-intercept. Find x and y-intercepts. 1) 3x + y = -7

Graph the equation by finding the slope and y-intercept. Find x and y-intercepts. 1) 3x + y = -7
Transcript text: Graph the equation by finding the slope and $y$-intercept. Find $x$ and $y$-intercepts. 1) $3 x+y=-7$
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Solution

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Solution Steps

Step 1: Rewrite the equation in slope-intercept form

The given equation is \(3x + y = -7\). To find the slope and \(y\)-intercept, we need to rewrite it in the slope-intercept form \(y = mx + b\).

\[ y = -3x - 7 \]

Step 2: Identify the slope and \(y\)-intercept

From the equation \(y = -3x - 7\), the slope \(m\) is \(-3\) and the \(y\)-intercept \(b\) is \(-7\).

Step 3: Find the \(x\)-intercept

To find the \(x\)-intercept, set \(y = 0\) and solve for \(x\).

\[ 0 = -3x - 7 \\ 3x = -7 \\ x = -\frac{7}{3} \approx -2.3333 \]

Final Answer

  • Slope: \(-3\)
  • \(y\)-intercept: \(-7\)
  • \(x\)-intercept: \(-\frac{7}{3} \approx -2.3333\)

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