Answers:
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Explanation:
1)
For any vertical line, the slope is always undefined. Recall that slope = rise/run. For a vertical line, the run is 0 because there is no left or right movement. This leads to a division by zero error. The vertical line is also parallel to the y axis, meaning that there isn't a y intercept whenever the line isn't directly on top of the y axis.
The equation of this vertical line is x = 3 as all points on this line have the same x coordinate of 3.
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2)
We can use the slope formula for the points [tex](x_1,y_1) = (-1,-4) \ \text{ and } \ (x_2,y_2) = (3,4)[/tex]
So,
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{4-(-4)}{3-(-1)}\\\\m = \frac{4+4}{3+1}\\\\m = \frac{8}{4}\\\\m = 2\\\\[/tex]
The slope is 2.
The y intercept is -2 as this is the location where the diagonal line crosses the y axis.
The equation of this line is y = 2x-2.
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3)
Same idea as problem 2.
[tex](x_1,y_1) = (-2,3)\\\\(x_2,y_2) = (3,-2)\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{-2-3}{3-(-2)}\\\\m = \frac{-2-3}{3+2}\\\\m = \frac{-5}{5}\\\\m = -1\\\\[/tex]
The slope is -1.
The y intercept is 1 because the line cuts through 1 on the y axis.
The equation is y = -1x+1 which is the same as y = -x+1.
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4)
Pick any two points from the table. Each column represents a different (x,y) ordered pair point. Those two points selected are then plugged into the slope formula. I'll pick the first two columns.
[tex](x_1,y_1) = (1,-2)\\\\(x_2,y_2) = (2,-2)\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{-2-(-2)}{2-1}\\\\m = \frac{-2+2}{2-1}\\\\m = \frac{0}{1}\\\\m = 0\\\\[/tex]
Notice how the y coordinates are the same, which leads to a difference of 0 up top and ultimately the slope itself is also 0. We have a horizontal flat line here. All horizontal lines have a slope of 0.
The y intercept is -2 because all y values for this function are the same.
The equation is y = 0x-2 which is the same as y = -2.
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5)
Again I'll pick the first two columns to plug into the slope formula, but you can pick any two columns you prefer.
[tex](x_1,y_1) = (-3,11)\\\\(x_2,y_2) = (-1,3)\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{3-11}{-1-(-3)}\\\\m = \frac{3-11}{-1+3}\\\\m = \frac{-8}{2}\\\\m = -4\\\\[/tex]
The slope is -4.
Use this slope value, along with any column from the table to form the (x,y) point, to plug into the slope intercept form below. I'll use the first column
y = mx+b
11 = -4*(-3)+b
11 = 12+b
11-12 = b
-1 = b
b = -1
The y intercept is -1.
The equation is y = -4x-1.
