Would love it if absolute detail is giving on how to solve the question
Calculate the slope between (6,9) and (-3,9)
m = (y2- y1)/(x2 - x1) = (9 - 9)/(6 - (-3)) = 0/9 = 0
The slope is a horizontal line at y = 9.
Data: for (x,y) => A(1) = (6,9); A(2)=(-3,9)
Def: slope = [y(2)-y(1)]/[(x(2)-x(1)], to obtain the slope you can chose as point 1 or 2 the A(1) or A(2) coordinate.
if point y(1)=y(2), then y(2)-y(1)=0 and your slope should be 0, if and only if x(1)=/= x(2), if x(2)=x(1) your slope is undefined!!!!
if y(2)=y(1) = 9
X(2)=-3; x(1)=+6, then [x(2)-x(1)] = -9 =/= 0
then : your slope = 0
The slope of a line (m) is defined as rise (change in y values) over run (change in x values). Mathematically, the slope can be described as: m = (y2 - y1)/(x2 - x1)
For this question, you can label the points 1 (6,9) and 2 (-3,9). This means that x1=6, y1=9, x2=-3, and y2=9. From there, you plug the x and y values into the equation for slope. This gives you:
m = (9 - 9)/(-3 -6) which simplifies to
m = 0/-9 = 0
This tells you that the slope equals zero. This means that the change in y values for the line is zero, and you have a horizontal line, y = 9 (George is correct). It might be helpful for you to draw a graph with x and y axes, then plot these two points. When you connect the two points with a straight line, you will see the horizontal line y = 9.
As a general rule:
A line with a slope of 0 is a horizontal line.
A line with an undefined slope (where the change in x values is zero) is a vertical line.
A line with a positive slope (greater than zero) is a diagonal line pointing up on the right side.
A line with a negative slope (less than zero) is a diagonal line pointing down on the right side.
I hope this helps!