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RideAnS [48]
3 years ago
6

Is the relationship shown by the data linear? How can you tell if it is or is not? If so, model the data with an equation.

Mathematics
1 answer:
yuradex [85]3 years ago
6 0

Hello from MrBillDoesMath!

Answer:    The relationship is linear. The equation is y = 2x + 19

Discussion:

When x changes from -7 to -5 ( and increment of of +2),  y changes from 5 to 9 ( an increment of +4). When x changes from 5 to -3 (an increment of +2) , y changes from 9 to 13 (an increment of +4)... and so on.....

So far, when x changes by 2, y changes by 4.  This means the data falls on a line (so is linear). In fact,

(change in y) /  (change in x) = 4/2 = 2 =  slope of line.

so  y = 2x + b. As the line passes through the point ( -7, 5)

5 = 2 (-7) + b    or

5 = -14 + b       or ( adding 14 to both sides)

5 + 14 = 19  = b.

Hence the equitation the line is  y = 2x + 19

Thank you,

MrB

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2.

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3 years ago
Find the equation of the line that passes through the following two points: (3, -7) and (7, 2)
Wittaler [7]

Answer:

y=\frac{9}{4}x-\frac{55}{4}

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: \frac{y2-y1}{x2-x1}

Given points: (3, -7), (7, 2)

(3, -7) = (x1, y1)

(7, 2) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the slope formula:

\frac{2-(-7)}{7-3}

Simplify:

2 - (-7) = 2 + 7 = 9

7 - 3 = 4

\frac{9}{4}

The slope is \frac{9}{4}.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (7, 2)) into the equation and solve for b:

2=\frac{9}{4}(7)+b

2=\frac{63}{4}+b

-\frac{55}{4} =b

The y-intercept is -\frac{55}{4}.

Now that we know the slope and the y-intercept, we can write the equation:

y=\frac{9}{4}x-\frac{55}{4}

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3 years ago
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