Hey there! I'm happy to help!
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<u>INTRODUCTION TO SLOPE INTERCEPT FORM</u>
Slope intercept form an equation for a line that includes a point, the slope, and the y-intercept. This equation can be modeled below.
y=mx+b
In this equation, m is the slope and b is the y-intercept.
The slope is how steep the line is.
The y-intercept is where the line runs into the y-axis.
Why do we even have this equation?
Well, we use it to build lines. It shows how the points of the line are oriented in terms of the two axes. If you knew that the x-value of a point was 1, you would plug it into the equation (if you had the values for x and b) and you would figure out what the y was. You would then plot this point and then do it with other numbers and then you would connect the dots and you have your line!
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<u>PUTTING THE EQUATIONS IN SLOPE INTERCEPT FORM</u>
As you can see, not all of our equations are in slope intercept form. A and C are in slope intercept form, but B and D are not. Let's solve for y in these equations.
OPTION B
-4x+2y=-6
We add 4x to both sides.
2y=4x+-6
We divide both sides by two.
y=2x-3
OPTION D
2x-3y=-9
We subract 2x from both sides.
-3y=-2x-9
We divide both sides by -3.
y=-2/3x+3
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<u>INTERPRETING THE GRAPH</u>
Y-INTERCEPTS
As we have said before, the y-intercept is where the line hits the y-axis. As we can see on the graph, the line hits the y-axis (the vertical one) below zero (zero is the center). This means that the y-intercept is negative.
Let's look at our equations. The y-intercept is the constant (the number without a variable). We know that our y-intercept has to be negative.
A: y=3x-2
B: y=2x-3
C: -10
D: -2/3x+3
As we see, A,B, and C have negative y-intercepts. These can move on. D does not. It is positive. Therefore, we can eliminate D as an option.
SLOPES
Let's look at the slope of each line. Our slope has to be positive because our line is sloping upwards.
A: y=3x-2
B: y=2x-3
C: 0 (the slope has to be zero because our y-value will always be -10 according to the equation. This is a flat, horizontal line so it will have a slope of zero. )
We see that both 3 and 2 make sense as slopes because they are both positive. C does not because C is a flat line. So, we can eliminate C as an option.
This leaves us with the equations A and B, which both make sense because they have positive slopes and negative y-intercepts. There is nothing else we can do to disprove any of them.
Therefore, the answer is A. y=3x-2 and B. -4x+2y=-6.
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I hope that this helps! Have a wonderful day! :D
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