Questions: Find the slope and the y-intercept of the line. -5x-4y=-8 Write your answers in simplest form. slope:

Transcript text: Find the slope and the $y$-intercept of the line. \[ -5 x-4 y=-8 \] Write your answers in simplest form. slope: $\square$

Solution

Solution Steps

Step 1: Rewrite the equation in slope-intercept form

The slope-intercept form of a line is $ y = mx + b $, where $ m $ is the slope and $ b $ is the $ y $-intercept. Start by isolating $ y $ in the given equation: \[ -5x - 4y = -8 \]

Step 2: Solve for $ y $

Add $ 5x $ to both sides of the equation: \[ -4y = 5x - 8 \]

Now, divide both sides by $ -4 $ to solve for $ y $: \[ y = -\frac{5}{4}x + 2 \]

Step 3: Identify the slope and $ y $-intercept

From the equation $ y = -\frac{5}{4}x + 2 $, the slope $ m $ is $ -\frac{5}{4} $, and the $ y $-intercept $ b $ is $ 2 $.

slope: $-\frac{5}{4}$

Final Answer

The slope is $\boxed{-\frac{5}{4}}$ and the $ y $-intercept is $\boxed{2}$.

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