Question

Find the equation of the straight line passing through each of the following pairs of points.

( 11 , 13) and (14, 19)

Answer 1

Answer: y = 2x - 9

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Step-by-step explanation:

Let's find the slope of the line through the given points.

`(x_1,y_1) = (11,13) \text{ and } (x_2,y_2) = (14,19)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (19 - 13)/(14 - 11)\\\\m = (6)/(3)\\\\m = 2\\\\`

The slope is 2.

Now apply point-slope form and solve for y as shown in the steps below.

`y - y_1 = m(x - x_1)\\\\y - 13 = 2(x - 11)\\\\y - 13 = 2x + 2*(-11)\\\\y - 13 = 2x - 22\\\\y = 2x - 22 + 13\\\\y = 2x - 9\\\\`

The answer is y = 2x - 9

It's of the form y = mx+b

• m = 2 = slope
• b = -9 = y intercept

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Check:

Let's plug in x = 11.

We should get y = 13 as a result because of the point (11,13)

So,

y = 2x-9

y = 2*11-9

y = 22 - 9

y = 13

This confirms y = 2x-9 goes through (11,13)

Follow similar steps to show that x = 14 leads to y = 19.

I'll let you do this part.