The slope of a line is –2 and its y-intercept is (0, 3). What is the equation of the line that is parallel to the first line and passes through (2, 2)?

Question

i need help with my math cause im having a lot of troubles and i really could use some help please.

Answer 1

The equation of the first line in slope-intercept form is y=-2x+3.

The equation of any parallel line, a line with same slope, is y=-2x+b, where b is its y-intercept

The line passes through (2,2) and has slope -2. 

If you walk back 2 steps in x to the y-axis, in order to stay on the line you have to go up 4 steps from y=2 to y=6. 

You are walking backwards on a line going down to the right, or up to the left.   y=-2x+6

Answer 2

Hi Cody;

The slope of the first line is -2.

The slope of the line parallel to such is also -2.

(The slope of the line perpendicular to such is 1/2.)

The equation of such first line can be established by using the slope-intercept formula...

y=mx+b

m=slope

b=y-intercept, value of y when x=0.

y=-2x+3

The y-intercept of the first line is a non-issue in establishing the equation of the second line except for the fact that the y-intercept must be different.

This the point-slope formula...

y-y₁=m(x-x₁)

Let's apply the slope and one point provided...

y-2=-2(x-2)

y-2=-2x+4

Let's add 2 to both sides...

2+y-2=-2x+4+2

y=-2x+6