Hi student, let me help you out!
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Part 1.
What is the slope of the line [tex]\mathtt{y=4-2x}[/tex]?
- slope = -2
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Part 2.
What is the slope of the line that is parallel to the line [tex]\mathtt{y=4-2x}[/tex]?
- slope = [tex]\mathtt{-2}[/tex]
[tex]\dag\mathtt{Drawing\:Conclusions}[/tex]
The slopes of parallel lines are identical.
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Part 3. Equation
Now that we've found the slope, we can easily find the equation.
Recall the point that the line contains: (2, -1).
Let's stick in its y-coordinate, -1, instead of y: [tex]\mathtt{-1=-2x+b}[/tex]
Do the exact same thing with x: [tex]\mathtt{-1=-2(2)+b}[/tex].
Upon simplifying, we obtain [tex]\mathtt{-1=-4+b}[/tex].
Now we should add 4 to both sides: [tex]\mathtt{-1+4=b}[/tex].
Upon simplifying, we obtain [tex]\mathtt{3=b}[/tex]
- Incase you're wondering, "b" is the y-intercept.
∴, the equation of the line is [tex]\underline{\boxed{\mathtt{y=-2x+3}}}[/tex].
Hope this helped you out, ask in comments if any queries arise.
Best Regards!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\bold{Reach\:Far.\:Aim\:high.\:Dream\:big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{3}}[/tex]