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What is the equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form?

a. y = 1/2)x - 2/2
b. y = 1/2x +2/2
c. y = 2x - 1/2
d. y = 8x + 3

1 Answer

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Final answer:

The equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form is y = 4x.

Step-by-step explanation:

To find the equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form, we first need to find the slope of the line. The slope, denoted as 'm', can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates from the two points into the formula, we get:

m = (12 - 20) / (3 - 5) = -8 / -2 = 4

So the slope of the line is 4. Now, we can use the slope-intercept form of the equation, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Since we already have the value of 'm' (4), we can substitute one of the given points (for example, (5, 20)) into the equation to solve for 'b'.

20 = 4(5) + b

20 = 20 + b

b = 0

Therefore, the equation of the line passing through the points (5, 20) and (3, 12) in slope-intercept form is:

y = 4x

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