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Ray Of Light [21]
3 years ago
7

What is the standard form of the points (-3,4) (2,-6)

Mathematics
1 answer:
Bas_tet [7]3 years ago
6 0

The standard form equation of the line connecting the two points is 2x +  y = -2

Linear equation in a standard form is given as Ax + By = C

where,

A, B, and C are constants or numbers

x and y are the variables.

To solve this problem, the following steps would be taken:

Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)

slope (m) = \frac{y_2 - y_1}{x_2 - x_1}

where,

(x_1, y_1) = (-3,4)\\(x_2, y_2) = (2,-6)

Substitute

slope (m) = \frac{-6 - 4}{2 -(-3)} \\m = \frac{-10}{5}\\m = -2

Step 2: Find the y-intercept (b) of the line by substituting (x, y) = (-3,4) and m = -2 into y = mx + b (slope-intercept form)

4 = -2(-3) + b\\4 = 6 + b\\4 - 6 = 6 + b - 6\\-2 = b\\b = -2

Step 3: Write the equation of the line in slope-intercept form by substituting m = -2 and b = -2 into y = mx + b

y = -2x + (-2)\\y = -2x - 2

Step 4: Rewrite the equation in standard form (Ax + By = C)

y = -2x - 2\\

Add 2x to both sides

2x + y = -2x - 2 + 2x\\2x +  y = -2

The standard form equation of the points (-3,4) and (2,-6) is 2x +  y = -2

Learn more about standard form of two points of a linear equation here:

brainly.com/question/18446164

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For this case we convert the mixed numbers to fractions:

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We subtract to know how much more time it takes Mike:

\frac {16} {5} - \frac {4} {3} = \frac {48-20} {15} = \frac {28} {15}

So, Mike takes \frac {28} {15} hours more than Dwight to walk the road.

Answer:

Mike takes\frac {28} {15}hours longer than Dwight to walk the road.

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