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write the equation of the line in fully simplified slope-intercept form…. pleaseee help

Write The Equation Of The Line In Fully Simplified Slopeintercept Form Pleaseee Help class=

Sagot :

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Answer:

y = -x + 2

Step-by-step explanation:

Given the two points on the graph, (-2, 4) and (0, 2), we can start by solving for the slope of the line.

Let (x₁, y₁) = (-2, 4)

     (x₂, y₂) = (0, 2)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 4) / [0 - (-2)]

m = -2/ (0 + 2)

m =  -2/2  = -1

Therefore, the slope of the line is -1.

Next, we need to determine the y-intercept of the line, which is the point on the graph where it crosses the y-axis. Upon observing the graph, it is evident that it crosses the y-axis at point (0, 2), which happens to be one of the points we used to solve for the slope. Its y-coordinate, y = 2, is what we will use as the value of b in the slope-intercept form, y = mx + b.

Therefore, given the slope, m = -1, and the y-intercept, b = 2, the equation of the line is:  

y = -x + 2

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