46) through: (3, -5), perp. to y=-x-3
find slope intercept form

y = x - 8

Step-by-step explanation:

The equation of the straight line which is perpendicular to the straight line y = -x -3, will be y = x + c' (1), where c' is a constant.

{This is because the product of the slopes of two mutually perpendicular straight line is -1}

Now, (3,-5) point satisfies equation (1).  

Hence, -5 = 3 +c', ⇒c' = -8.

Therefore, the equation of the required straight line in slope-intercept form is y = x - 8 (Answer)

{Note: The slope-intercept form of a straight line is y = mx + c, where m is the slope of the line i.e. tanФ, and c is the length of y-axis intercept.}