Question
4))
, A line has a slope of
and a
-intercept of
, Write its equation in slope-intercept
form.
41)
, Write your answer using integers, proper fractions, and improper fractions in
simplest form.
form.
41)
simplest form.
Ask by Turner Ford. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
4) The equation of the line in slope-intercept form is
.
41) The simplified form of
is 2.
Solution
Sure, let’s address both of your questions step by step.
4) Writing the Equation of a Line in Slope-Intercept Form
Given:
- Slope (m):
- Y-intercept (b):
Slope-Intercept Form:
The slope-intercept form of a linear equation is:
The slope-intercept form of a linear equation is:
Plugging in the Given Values:
Final Equation:
41) Simplifying
Expression:
Simplification Steps:
-
Understanding the Expression:
- The square of the square root of a number returns the original number.
-
Applying the Property:
-
Applying to Your Expression:
Final Answer:
If you have any more questions or need further clarification, feel free to ask!
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To write the equation of a line in slope-intercept form (which is
), we plug in the slope and the
-intercept. Here, the slope
is
and the
-intercept
is
. Therefore, the equation of the line is
.
Now, let’s focus on the second part. The expression
suggests using the square root of 2 in an exponent. If you’re representing powers, for instance, you could write this as
. This aligns with integers, proper fractions, and improper fractions, even if the original expression isn’t purely a fraction; it showcases how roots translate into fractional exponents, highlighting another mathematical relationship that can lead to fascinating insights!