Questions: Find the slope-intercept form of the linear function f whose graph passes through the given pair of points. 3) (-6,-3) and (-8,-7) A) f(x)=-2x+9 B) f(x)=2x+9 C) f(x)=2(x+6)-3 D) f(x)=-2x-9

Find the slope-intercept form of the linear function f whose graph passes through the given pair of points.
3) (-6,-3) and (-8,-7)
A) f(x)=-2x+9
B) f(x)=2x+9
C) f(x)=2(x+6)-3
D) f(x)=-2x-9

Transcript text: Find the slope-intercept form of the linear function f whose graph passes through the given pair of points. 3) $(-6,-3)$ and $(-8,-7)$ A) $f(x)=-2 x+9$ B) $f(x)=2 x+9$ C) $f(x)=2(x+6)-3$ D) $f(x)=-2 x-9$

Solution

Solution Steps

To find the slope-intercept form of the linear function $ f $ that passes through the given points $(-6, -3)$ and $(-8, -7)$, we need to:

Calculate the slope $ m $ using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $.
Use the point-slope form $ y - y_1 = m(x - x_1) $ to find the equation of the line.
Convert the equation to slope-intercept form $ y = mx + b $.

Step 1: Calculate the Slope

To find the slope $ m $ of the line passing through the points $(-6, -3)$ and $(-8, -7)$, we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points: \[ m = \frac{-7 - (-3)}{-8 - (-6)} = \frac{-7 + 3}{-8 + 6} = \frac{-4}{-2} = 2 \]

Step 2: Calculate the Y-Intercept

Using the slope-intercept form $ y = mx + b $, we can solve for $ b $ (the y-intercept) by substituting one of the points and the slope $ m $: \[ -3 = 2(-6) + b \] Solving for $ b $: \[ -3 = -12 + b \implies b = 9 \]

Step 3: Form the Equation

Now that we have the slope $ m = 2 $ and the y-intercept $ b = 9 $, we can write the equation of the line in slope-intercept form: \[ f(x) = 2x + 9 \]