How would you explain these equations??

Question

I need to explain how I was able to match these 2 equations with the correct graph and I'm having a hard time coming up with the words. I know how to graph them and have the answers but need help explaining how I know this.

1. y = -x + 1
2. y = x + 1

Answer 1

y = mx + b
m = slope, b = y-intercept

1) m = -1 and b = 1
Crosses the y-axis at 1.
The slope is -1, so that means as you move right, you move down. Every time you move down 1, you move to the right by 1.

2) m = 1 and b = 1
This one crosses the y-axis at 1 as well.
However, the slope is 1, so as you move to the right, you move up. Every time you move up 1, you move to the right by 1.

Answer 2

1. These are in y-int form: y = mx + b -- where m = slope and b = the y-intercept. Therefore, you know the slope is -1 b/c that is the coefficient in front of the "x". You also know the y-intercept is 1.

2. Here you know the slope is 1 and the y-intercept is 1.

You can justify their slopes by picking a point on the graph and going up 1 and over 1 = slope. (slope = rise/run)

NOTE: These lines are perpendicular at the y-intercept, 1.

Answer 3

The coefficient of the x is the slope. For the first equation, slope = rise/run = -1, so for every step you take in the x-direction, you go down one step in the y-direction. For the second equation, the situation is reversed.

Both equations have a y-intercept of 1, because when you plug in a value of 0 for x, the equations turn into y = 0 + 1, or simply y = 1.

Hope that helps!

Answer 4

These are straight line equations of the form y=mx + b , where m is the slope of the line and b is the y-intercept.
1. -1 =m and +1 = b
2. +1 =m and +1 = b

Answer 5

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There are several obvious things you could say about those two lines. One is that they are perpendicular to each other. You can tell this because the slopes are opposite reciprocals of one another.

The other thing you can tell is that they intersect at the point (0,1), because they both have that as their y-intercept.

The main thing, though, if you want to match each one up with its respective graph is that one has a negative slope of -1 (sloping downward from left to right) and one has a postiive slope of 1 (sloping upward from left to right).

That should put you right!
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Answer 6

You could say that they intersect at (0,1) , they share a y intercept of 1, they are perpendicular to each other (they form a right angle) and that the two slopes are negative reciprocals of each other

Answer 7

i would start by explaining slope intercept form

y = -x + 1 first point is (0,1) and the slope is -1

y = x + 1 first point is (0,1) and the slope is +1