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const2013 [10]
2 years ago
9

Write an equation in slope-intercept form that goes through (12, 4) and (20,8).

Mathematics
1 answer:
spayn [35]2 years ago
4 0

Answer:

Equation in slope-intercept form that goes through (12, 4) and (20,8) is: y = \frac{1}{2}x-2

Step-by-step explanation:

Given two points are:

(x_1,y_1) = (12,4)\\(x_2,y_2) = (20,8)

Slope intercept form of line is given as:

y = mx+b

Here m is the slope of the line and b is the y-intercept.

Slope of a line is calculated by the formula:

m = \frac{y_2-y_1}{x_2-x_1}

Putting the values

m = \frac{8-4}{20-12}\\m = \frac{4}{8}\\m=\frac{1}{2}

Putting the value of slope in slope-intercept form we get

y = \frac{1}{2}x+b

To find the value of b, any one point will be put in the equation

Putting the first point (12,4) in the equation

4 = \frac{1}{2}(12) + b\\4 = 6+b\\b = 4-6\\b = -2

Putting the value of b

y = \frac{1}{2}x-2

Hence,

Equation in slope-intercept form that goes through (12, 4) and (20,8) is: y = \frac{1}{2}x-2

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What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio? Negative one-eleventh
Elden [556K]

The location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is \frac{1}{11}.

The given parameters:

  • <em>Partition of the line segment = 5:6</em>

The total segment of the directed line segment from D to E in the given ratio of 5:6 is calculated as follows;

total segment = 5 + 6 = 11

The value of each partition on the directed line segment is calculated as follows;

partition = \frac{1}{11} \times distance

The distance between point D and point E is calculated as follows;

D = 5 - (-4)\\\\D = 5 + 4\\\\D = 9

The partition of the two points (D to E) is calculated as follows;

partition = \frac{1}{11} \times 9 = 0.82

Thus, we can conclude that, the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is \frac{1}{11}.

Learn more about partition of line segments here: brainly.com/question/4429522

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