Question
Question Write an equation of the line with the given slope, m , and y -intercept \( (0, \mathrm{~b}) \) \[ \begin{array}{l}\text { tines } \\ \mathrm{m}, \mathrm{b}=0\end{array} \] The equation is \( \square \).
Ask by Nichols Burgess. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = mx + b \).
Solution
The general equation of a line with slope \( m \) and y-intercept \( (0, b) \) is given by
\[
y = mx + b.
\]
Since the y-intercept is \((0, b)\), when \( x = 0 \) the equation becomes
\[
y = m(0) + b = b,
\]
which confirms the y-intercept. Therefore, the equation of the line is
\[
y = mx + b.
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
When the slope \( m \) is provided as 0, that means the line is horizontal! In this case, the equation of the line is simply \( y = 0 \). All points on this line have a y-value of 0, so it sits perfectly on the x-axis, stretching infinitely in both left and right directions. In real-world scenarios, a horizontal line like this could represent anything static—think of water level in a tank that's not rising or falling! So, if you were monitoring the temperature in a controlled environment that’s stable, your graph might just show a horizontal line at the constant temperature.
