Questions: Find the slope and the y-intercept of the line, 4 x-3 y=15 Write your answers in simplest form. slope: y-intercept:

Find the slope and the y-intercept of the line,
4 x-3 y=15

Write your answers in simplest form.
slope:
y-intercept:

Transcript text: Find the slope and the $y$-intercept of the line, \[ 4 x-3 y=15 \] Write your answers in simplest form. slope: $y$-intercept:

Solution

Solution Steps

To find the slope and the y-intercept of the line given by the equation \(4x - 3y = 15\), 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

We start with the equation of the line given by

\[ 4x - 3y = 15. \]

To find the slope and the y-intercept, we need to rewrite this equation in the slope-intercept form \(y = mx + b\).

Step 2: Solve for \(y\)

Rearranging the equation to isolate \(y\):

\[ -3y = -4x + 15 \]

Dividing through by \(-3\):

\[ y = \frac{4}{3}x - 5. \]

Step 3: Identify the Slope and Y-Intercept

From the equation \(y = \frac{4}{3}x - 5\), we can identify the slope \(m\) and the y-intercept \(b\):

Slope \(m = \frac{4}{3}\)
Y-intercept \(b = -5\)

Final Answer

The slope is \(\frac{4}{3}\) and the y-intercept is \(-5\).

\[ \boxed{\text{slope: } \frac{4}{3}, \text{ y-intercept: } -5} \]

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