Question 733928
The slopes of perpendicular lines multiply to yield {{{(-1)}}}.
 
The equation {{{y=-3x+4}}} represents a line that crosses they-axis at {{{y=4}}}  because when {{{x=0}}} --> {{{y=4}}}.
The line has {{{slope=-3}}} , meaning that as x increases by 1, y "increases" by -3 (meaning that it decreases by 3).
The line looks like this:
{{{drawing(300,400,-3,7,-4,10,
grid(1), blue(line(-3,13,3,-5)),
red(line(0,4,0,1)),red(line(0,1,1,1))
)}}} The blue-and-red triangle shows how an increase of 1 in x means an "increase" of -1 in y.
We can draw many perpendicular lines. I will draw a perpendicular line that goes through (0,4) like this
{{{drawing(300,400,-3,7,-4,10,
grid(1), blue(line(-3,13,3,-5)),
blue(triangle(0,4,1,4,1,1)),
red(line(0,4,0,1)),red(line(0,1,1,1)),
green(line(-3,3,12,8)),red(line(0,4,3,4)),
red(line(3,4,3,5))
)}}} The green-and-red triangle is the blue and-red triangle rotated {{{90^o}}}.
Its sides are perpendicular to the corresponding sides of the blue-and-red triangle.
That makes the blue and green lines perpendicular to each other.
The green-and-red triangle shows that for the green line, an increase of 3 in x translates into an increase of 1 in y, meaning that the slope of the green line is {{{1/3}}} .
The equation of the green line is {{{y=(1/3)x+4}}} .
The slopes of perpendicular lines multiply to yield {{{(-1)}}} because in those rotated right triangles the ratio of vertical leg to horizontal leg is reversed (the ratios are reciprocals), but if one of the (change in y)/(change inx) ratios in positive, the other must be negative, so the product will be not 1, but -1.