Given the following linear function, which represents the correct way to type the equation into DESMOS?

Question image

Understand the Problem

The question is asking which of the given options correctly represents a linear function formatted for entry into the DESMOS graphing calculator, based on the equation provided.

Answer

The correct option is: $$ y = -3(x - 5) - 1 $$
Answer for screen readers

The correct representation to type into DESMOS is:
$$ y = -3(x - 5) - 1 $$

Steps to Solve

  1. Start with the original equation We have the equation:
    $$ y + 1 = -3(x - 5) $$

  2. Isolate (y) on one side To convert it to slope-intercept form (i.e., (y = mx + b)), we need to isolate (y).
    Subtract 1 from both sides:
    $$ y = -3(x - 5) - 1 $$

  3. Distribute the (-3) Now, distribute (-3) to both terms inside the parentheses:
    $$ y = -3x + 15 - 1 $$

  4. Combine like terms Combine the constant terms (15) and (-1):
    $$ y = -3x + 14 $$

  5. Rewrite for DESMOS compatibility The equation is now in slope-intercept form. To enter into DESMOS, we rearrange the expressions:
    The option that matches will typically be similar in form to the expanded version we derived.

The correct representation to type into DESMOS is:
$$ y = -3(x - 5) - 1 $$

More Information

This equation maintains the original slope and y-intercept when reformulated. The original function had a negative slope of (-3), which is reflected consistently across the correct options.

Tips

  • Incorrectly distributing: Ensure you properly distribute the negative coefficient to both terms inside the parentheses.
  • Sign errors: Be careful with signs when you add or subtract constants.

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