Question

Determine the equation for a line that passes through the point M(-7, 3) and

Answer 1

Answer:

y = 2x/7 + 5

Step-by-step explanation:

the first line is defined by

7x - 2y + 3 = 0

in the most common way to write this we need an equation like y = ...

so, we isolate the y-expression in the equation :

2y = 7x + 3

y = (7x + 3) / 2 = 7x/2 + 3/2

the factor of x is the slope of the line, which is expressed by the y/x ratio indicating how many units y will change, when x changes e.g. 1 unit.

7/2 means that y will change by 7 units for every change in x by 2 units.

the slope of a perpendicular line is inverse to the slope of the original line, which means x and y are simply trading places (original x / original y).

so, the perpendicular slope of 7/2 is 2/7 (when x changes by 7 units, then y changes by 2 units).

that means the equation for the perpendicular line is something like

y = 2x/7 + c

the c we determine by using the coordinates of the given point (x and y values).

3 = 2×(-7)/7 + c = 2×(-1) + c = -2 + c

c = 5

so, the complete equation of the perpendicular line is

y = 2x/7 + 5