Questions: Find the slope and y-intercept of the following linear equation. Express the y-intercept as a coordinate pair. -6x + 10y = -7

Find the slope and y-intercept of the following linear equation. Express the y-intercept as a coordinate pair. -6x + 10y = -7
Transcript text: Find the slope and $y$-intercept of the following linear equation. Express the $y$-intercept as a coordinate pair. \[ -6 x+10 y=-7 \]
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Solution

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Solution Steps

Step 1: Rewrite the Equation in Slope-Intercept Form

The given equation is \(-6x + 10y = -7\). To find the slope and y-intercept, we need to rewrite this equation in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2: Isolate the y-Term

First, isolate the \(y\)-term by adding \(6x\) to both sides of the equation: \[ -6x + 10y + 6x = -7 + 6x \] \[ 10y = 6x - 7 \]

Step 3: Solve for y

Next, divide every term by 10 to solve for \(y\): \[ y = \frac{6}{10}x - \frac{7}{10} \] \[ y = \frac{3}{5}x - \frac{7}{10} \]

Step 4: Identify the Slope and y-Intercept

From the equation \(y = \frac{3}{5}x - \frac{7}{10}\), we can identify the slope \(m\) and the y-intercept \(b\):

  • Slope \(m = \frac{3}{5}\)
  • y-Intercept \(b = -\frac{7}{10}\)

Final Answer

  • Slope \(m = \frac{3}{5}\)
  • y-Intercept as a coordinate pair: \((0, -\frac{7}{10})\)
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