Question

indicate the equation of the given line in standard form, the line containing the hypotenuse of right triangle ABC where A(-5,5), B(1,1) C(3,4) are the vertices

Answer 1

Refer to the figure shown below.

The hypotenuse passes through the points (3,4) and (-5,5).
Calculate the slope.
m = (5-4)/(-5-3) = -1/8

In slope-intercept form, the equation of the hypotenuse is
$\frac{y-4}{x-3} = -\frac{1}{8}$
Cross multiply.
8(y-4) = -(x-3)
8y - 32 = -x + 3
8y = -x + 35
y = -(1/8)x + 35/8

Answer:
$y=- \frac{1}{8}x + \frac{35}{8}$