If $$ f(x) $$ is a linear function, $$ f(-3)=-5 $$, and $$ f(4)=0 $$, find an equation for $$ f(x) $$. $$ f(x)= $$ Question Help: Video D post to forum

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UpStudy AI · Accepted Answer

1. Write the general form of the linear function:
   $$
   f(x) = mx + b
   $$

2. Use the given condition $$ f(-3) = -5 $$:
   $$
   m(-3) + b = -5 \quad \Rightarrow \quad -3m + b = -5 \quad \text{(Equation 1)}
   $$

3. Use the given condition $$ f(4) = 0 $$:
   $$
   m(4) + b = 0 \quad \Rightarrow \quad 4m + b = 0 \quad \text{(Equation 2)}
   $$

4. Subtract Equation 1 from Equation 2 to eliminate $$ b $$:
   $$
   (4m + b) - (-3m + b) = 0 - (-5)
   $$
   $$
   4m + b + 3m - b = 5
   $$
   $$
   7m = 5 \quad \Rightarrow \quad m = \frac{5}{7}
   $$

5. Substitute $$ m = \frac{5}{7} $$ into Equation 2 to solve for $$ b $$:
   $$
   4 \left(\frac{5}{7}\right) + b = 0 \quad \Rightarrow \quad \frac{20}{7} + b = 0 \quad \Rightarrow \quad b = -\frac{20}{7}
   $$

6. Write the final equation of the linear function:
   $$
   f(x) = \frac{5}{7}x - \frac{20}{7}
   $$
$$ f(x) = \frac{5}{7}x - \frac{20}{7} $$

If is a linear function, , and , find an equation for .

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If is a linear function, , and , find an equation for . Question Help: Video D post to forum