Questions: A line has slope 3/4 and passes through the point (8,-3). By substituting into the equation y=mx+b, find the value of b for this line.

Transcript text: 42. A line has slope $\frac{3}{4}$ and passes through the point $(8,-3)$. 42a By substituting into the equation $y=m x+b$, find the value of $b$ for this line. Enter your next step here

Solution

Solution Steps

Step 1: Identify the given information

We are given the slope $ m = \frac{3}{4} $ and a point on the line $ (8, -3) $.

Step 2: Substitute the given information into the slope-intercept form

The slope-intercept form of a line is given by: \[ y = mx + b \] Substitute $ m = \frac{3}{4} $, $ x = 8 $, and $ y = -3 $ into the equation: \[ -3 = \frac{3}{4}(8) + b \]

Step 3: Solve for $ b $

First, calculate $ \frac{3}{4} \times 8 $: \[ \frac{3}{4} \times 8 = 6 \] Now substitute back into the equation: \[ -3 = 6 + b \] Subtract 6 from both sides to solve for $ b $: \[ b = -3 - 6 \] \[ b = -9 \]

Final Answer

\[ \boxed{b = -9} \]

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