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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)?

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2 Answers

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
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