Question

“The line that passes through point H has the equation y=-2x -3”

“The equation of the line parallel to the given line that passes through point g is”

Please help.

Answer 1

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