Answer:
Step-by-step explanation:
Generally
The equation of a line is given as
y = mx + c
Where
m is the slope
c is the intercept on y axis
Note: if two lines are parallel, their slopes are equal
I.e M1 = M2 =m
If two lines are perpendicular, then, their slopes are given as
M2 = - 1/M1
Given that,
The line that pass through the point H has an equation
y = -2x-3
From equation of a line, we know that, the slope of the line that passes through H is -2
m = -2
We want to find the equation of a line parallel to line that passes through H
If the line we want to find is parallel to the given line, then, their slope are equal,
So, the slope of line that passes through point G is m=-2
So, the equation of the line that passes through point G is
y = mx + c, m=-2
y = -2x + c
So, we need to find c, so, using the point G it passes through,
G = (2,1) I.e x = 2 and y = 1
y = -2x + c.
1 = -2(2) + c
1 = -4 + c
1+4 = c
c = 5
So, the equation of the line that passes through G becomes
y = -2x + 5
