Given the following linear function, which represents the correct way to type the equation into DESMOS?
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
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Start with the original equation We have the equation:
$$ y + 1 = -3(x - 5) $$ -
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:
$$ y = -3(x - 5) - 1 $$ -
Distribute the (-3) Now, distribute (-3) to both terms inside the parentheses:
$$ y = -3x + 15 - 1 $$ -
Combine like terms Combine the constant terms (15) and (-1):
$$ y = -3x + 14 $$ -
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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