Question

The slope and Y intercept of (1,0) and (3,6) in slope-intercept form.

Answer 1

Answer: y = 3x-3

slope = 3

y intercept = -3

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Explanation

Let's find the slope

`\text{Given Points: }(x_1,y_1) = (1,0) \text{ and } (x_2,y_2) = (3,6)\\\\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 = (6 - 0)/(3 - 1)\\\\m = (6)/(2)\\\\m = 3\\\\`

The slope is 3 which can be thought of as 3/1.

It means "go up 3, then right 1".

Now apply point-slope form.

`\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-0 = 3(\text{x}-1)\\\\\text{y} = 3(\text{x}-1)\\\\\text{y} = 3\text{x}-3\\\\`

The last equation is of the format y = mx+b

m = 3 = slope

b = -3 = y intercept

Answer 2

Slope: 3

Slope-intercept form: y=3x-3

Explanation:

To find the slope, use the equation:
`(y_(2) -y_(1))/(x_(2) -x_(1))`

Plug in the values:
`(6-0)/(3-1)`

Which simplies to:
`(6)/(2)` or 3

To find the slope-intercept form, use the equation: y=mx+b

Plug in the slope in m: y=3x+b

Plug in one of the intercept values (1,0): 0=3(1)+b

b=-3

Thus, the slope-intercept form is: y=3x-3