find the slope intercept form and the point slope

Question

the line parallel to x=-4 going through points (-5,10)

Answer 1

x=-5 is parallel to x=-4. They're both vertical lines, with undefined slope, or infinite slope

x=-5 goes through the point (-5, 10). it goes through any point with an x coordinate = -5

in point slope form, it doesn't make sense as m = slope is undefined.

y-y1 = m(x-x1) through the point (x1,y1) with slope=m

y-10 = m(x--5)

y-10 = mx + 5m (y-10 = zero compared to the infinite

terms on the right side, m is infinite)

0 = mx +5m

mx =-5m

x =-5

slope intercept form

is y=mx + b where b= y intercept and m = slope

x=-4 and x=-5 are vertical lines which never intersect the y axis so there is no y intercept. It's not 0 or any real number

maybe set b = 5m where m is infinitely large Perhaps in curved space two parallel lines may intersect at a distance of infinity, at (0,5m) where m= infinity

y= mx + 5m, then y is equivalent to zero compared to m

0 =mx+5m

mx=-5m

x =-5

but there really is no slope intercept form for x=-5