Answer:
See step by step explanation or see diagram.
Explanation:
Hi!
So, we're asked to find a line that is parallel to the given line and passes through a point.
We're going to use slope-intercept form.
y=mx+b
M is slope and b is y-intercept
Start!: Find a line that is parallel to y= -2x +4 and passes through (-4,7)
Parallel lines have the same slope . We can change slope-intercept form to reflect that.
y=-2x + b
Now, we need to find b (the y-intercept). We can do this by plugging in the coordinates of the point that we were given.
7= -2 (-4) + b
7 = 8 +b
b = -1
Next, change the equation to reflect that.
y = -2x - 1.
So, go right.
This time, the point is (2,1) and the line is y= -x - 4.
The slope of a line parallel to y = -x -4 is -1.
y= -1x+b
Plug in the points:
1 = -1 (2) +b
1 = -2 +b
b = 3
Finish the equation.
y = -x + 3.
Go diagonally.
This time, the point is (-6,1) and the line is y = 1/2x +1 .
The slope of the parallel line will be 1/2.
y= 1/2x +b
Plug in points:
1 = 1/2 (-6) + b
1 = -3 +b
b = 4
y = 1/2x + 4
Go down.
This time, the point is (2,0) and the line is y= 3/2x+5
Slope of parallel line: 3/2
y = 3/2x+b
Subsitute points in.
0 = 3/2(2) + b
0 = 3 + b
b = -3
y = 3/2x -3
Go left.
This time, the point is (-1,-5) and the line is y=2x-9
Slope of parallel line: 2
y=2x+b
Substitute points:
-5 = 2(-1) + b
-5 = -2 + b
b = -3
y= 2x -3
Go diagonally.
This time, the point is (-9, -8) and the line is y= 1/3x+3
Slope of parallel line: 1/3
y = 1/3x+b
-8 = 1/3 (-9) +b
-8 = -3 +b
b= -5
y=1/3x-5
Go up.
This time, the point is (4,3) and the line is y= x +6
SOPL (slope of parallel line): 1
y=x+b
3 = 4 + b
b = -1
y=x-1
Go right.
This time, the point is (-2, -8) and the line is y=3x-1
SOPL = 3
y= 3x+b
-8 = 3(-2) +b
-8 = -6 + b
b = -2
y=3x-2
Go down.
This time, the point is at (1,4) and the line is y=-2x-1
SOPL: -2
y= -2x + b
4 = -2 (1) +b
4 = -2 + b
b=6
y= -2x + 6
Go diagonally.
This time, the point is (4,11) and the line is y = -1/2x-5
SOPL: -1/2
y= -1/2x + b
11 = -1/2 (4) +b
11 = -2 +b
b=13
y= -1/2x+13
Finish!