Questions: Find the y-intercept and the slope of the line. 2x+3y=4 Write your answers in simplest form. y-intercept: slope:

Find the y-intercept and the slope of the line. 2x+3y=4 Write your answers in simplest form. y-intercept: slope:
Transcript text: Find the $y$-intercept and the slope of the line. \[ 2 x+3 y=4 \] Write your answers in simplest form. \begin{tabular}{ll|} $y$-intercept: \\ slope: \\ $\square$ \end{tabular}
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Solution

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Solution Steps

To find the slope and y-intercept of the line given by the equation \(2x + 3y = 4\), we need to rewrite the equation in the slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. This involves solving the equation for \(y\).

Step 1: Rewrite the Equation in Slope-Intercept Form

To find the slope and y-intercept of the line given by the equation \(2x + 3y = 4\), we first need to rewrite the equation in the slope-intercept form, \(y = mx + b\). This involves solving the equation for \(y\).

Step 2: Solve for \(y\)

Starting with the equation: \[ 2x + 3y = 4 \]

Subtract \(2x\) from both sides: \[ 3y = -2x + 4 \]

Divide every term by 3 to solve for \(y\): \[ y = -\frac{2}{3}x + \frac{4}{3} \]

Step 3: Identify the Slope and Y-Intercept

From the equation \(y = -\frac{2}{3}x + \frac{4}{3}\), we can identify the slope \(m\) and the y-intercept \(b\).

  • The slope \(m\) is \(-\frac{2}{3}\).
  • The y-intercept \(b\) is \(\frac{4}{3}\).

Final Answer

\[ \begin{align_} \text{y-intercept:} & \quad \frac{4}{3} \\ \text{slope:} & \quad -\frac{2}{3} \\ \end{align_} \]

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