Question 733928: How can I solve this? I don't understand at all... "Write an equation for a line perpendicular to y=-3x+4" Answer by KMST(5328) (Show Source):
The equation represents a line that crosses they-axis at because when --> .
The line has , meaning that as x increases by 1, y "increases" by -3 (meaning that it decreases by 3).
The line looks like this: 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 The green-and-red triangle is the blue and-red triangle rotated .
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 .
The equation of the green line is .
The slopes of perpendicular lines multiply to yield 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.
