Explanation:
from the first line s
y - 7 = 9/10 × (x - 4)
we only need the slope, which is 9/10.
the -7 did not disturb this. only if y had a factor different to 1, we would have to re-simplify the equation to get the slope.
remember, a slope expresses the ratio (y change / x change).
a perpendicular slope note turns the y/x ratio upside-down and flips the sign.
so, 9/10 turns into -10/9, which is the slope of the new line t.
we can use the point-slope form to incorporate the given point and get the y-intercept for the final slope-intercept equation :
y - 6 = -10/9 × (x - -6) = -10/9 × (x + 6) =
= -10/9 × x - 60/9 = -10/9 × x - 20/3
y = -10/9 × x - 20/3 + 6 = -10/9 × x - 20/3 + 18/3 =
= -10/9 × x - 2/3
the line t is
y = -10/9 × x - 2/3