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What is the equation of this graph?

What is the equation of this graph?-example-1
User Sestocker
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1 Answer

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Answer (assuming it is allowed to be written in slope-intercept form):


y = -(2)/(3) x + 1

Explanation:

When knowing a line's y-intercept and its slope, you can write its equation using slope-intercept form, or
y = mx + b.

1) First, find the slope of the line. Read the graph and look at the two points marked on the line - they are (0,1) and (3,-1). Use the slope formula
(y_2-y_1)/(x_2-x_1) , substitute the x and y values of those points, and solve:


((-1)-(1))/((3)-(0)) \\= (-1-1)/(3-0) \\= (-2)/(3)

Thus, the line's slope is
-(2)/(3).

2) Now, use the slope-intercept formula,
y = mx + b, to write an equation. Substitute the
m and
b for real values.

The
m represents the slope, so substitute
-(2)/(3) in its place. The
b represents the y-value of the y-intercept, or the point at which the line crosses the y-axis. Looking at the graph, we can see that the line intersects the y-axis at (0,1). Thus, substitute 1 for
b. This gives the following equation and answer:


y = -(2)/(3) x + 1

User Himura
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