Question

Hello can someone help

Answer 1

Answer: y = 2x-1

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Step-by-step explanation:

Let's find the slope.

`A = (x_1,y_1) = (4,7) \text{ and } B = (x_2,y_2) = (2,3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (3 - 7)/(2 - 4)\\\\m = (-4)/(-2)\\\\m = 2\\\\`

The slope is 2.

Then apply point-slope form

`\text{y} - \text{y}_1 = \text{m}(\text{x} - \text{x}_1)\\\\\text{y} - 7 = 2(\text{x} - 4)\\\\\text{y} - 7 = 2\text{x} + 2(-4)\\\\\text{y} - 7 = 2\text{x} -8\\\\\text{y} = 2\text{x} -8+7\\\\\text{y} = 2\text{x} -1\\\\`

The final answer is y = 2x-1

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Check:

Plug in x = 4. We should get y = 7 as the output.

y = 2x-1

y = 2*4-1

y = 8-1

y = 7

This verifies point A(4,7) is on the line.

Plug in x = 2. We should get y = 3 as the output.

y = 2x-1

y = 2*2-1

y = 4-1

y = 3

This verifies point B(2,3) is also on the line.

The answer is fully confirmed. You can use graphing software like Desmos or GeoGebra as a quick way to confirm.