Question

question 6 0.5 pts what is the equation of a line that goes through (6,1) and has a slope of zero? - ( x = 1 ) - ( x = 6 ) - ( y = 6 ) - ( y = 1 )

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. If the slope $m = 0$, the equation of the line becomes $y=(0)x + b$, or simply $y = b$.

Step2: Determine the value of $b$

The line passes through the point $(6,1)$. For a line with equation $y = b$, the $y$ - coordinate of every point on the line is $b$. Since the point $(6,1)$ is on the line, the $y$ - coordinate of this point is $1$. So, $b = 1$.

Step3: Write the equation of the line

Substituting $m = 0$ and $b = 1$ into the slope - intercept form $y=mx + b$, we get $y=0\times x+1$, which simplifies to $y = 1$.

We can also analyze the other options:

• The equations $x = 1$ and $x = 6$ are vertical lines (slope is undefined, not zero), so they cannot be the equation of a line with slope zero.
• The equation $y = 6$ would be a horizontal line, but it does not pass through the point $(6,1)$ (since the $y$ - coordinate of the point is $1$, not $6$).

Answer:

$y = 1$ (or in the multiple - choice context, the option corresponding to $y = 1$)