The equation for a line in point slope form is:
y - y1 = m*(x - x1)
For the point (-7,6) on the line, x1 = -7 and y1 = 6. We're also told that the slope, m, is zero. So lets plug those values into the equation:
y - 6 = 0*(x - (-7)) --> y - 6 = 0
or y = 6
Of course, any line that has a slope of zero is a horizontal line. Since we knew that the line passes through the point (-7,6), we already knew without doing the math that the equation had to be y = 6.
(-7, 6) and has a slope of m=0.
The slope intercept formula is:
y - y1 = m(x - x1) where (x1, y1) are points on your line and m = slope.
Plug into that formula with your given points
y - 6 = 0(x - -7)
y - 6 = 0
y = 6
Any line that passes through a point P (x1,y1) is given by the relation of the ratio of its y distance of any point Q(x,y) from the given point P(x1,y1) to the x distance Q to the point P is equal to its slope.
If Q(x,Y) and P(x1, y1) are the points.
(The vertical distance of Q from P measured parallel to y axis)/(the horizontal distance of Q from P measured parallel to xaxis) = slope.
(y-y1)/(x-x1)= slope. But the slope is given to be 0 (zero).
Therefore,(y-y1/(x-x1)=0 . Given x=-7 and y=6 to be the coordinates of the given point. Therefore,
y- 6=0 or y=6 . This is a straight line parallel to x axis and is at a distance of 6 units from x axis.
Tally : y=6, it obviously is true for all values of x axis. Therefore, for x=-7. Thus the given line passes through the point (-7,6)