Question

Write an equation of the line below.

Answer 1

Answer: y = -2x+3

Step-by-step explanation

The two marked points on the blue line are (0,3) and (5,-7)

Use the slope formula.

`\text{Given Points: }(x_1,y_1) = (0,3) \text{ and } (x_2,y_2) = (5,-7)\\\\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 = (-7 - 3)/(5 - 0)\\\\m = (-10)/(5)\\\\m = -2\\\\`

The slope is -2.

A slope of -2 or -2/1 means "down 2, right 1".

Following this motion pattern has us go from (0,3) to (1,1) to (2,-1) to (3,-3) to (4,-5) to (5,-7) and so on.

The y intercept is 3 as this is where the blue line crosses the y axis.

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We found the following

m = -2 = slope

b = 3 = y intercept

The template y = mx+b updates to y = -2x+3 which is the final answer.