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A student created this table to represent a linear relationship between x and y. X. Y-2. 10.0-1. 7.50. 5.01. 2.52. 0Write an equation of the line represented by the relationship between x and y shown in the table.

User Greg Veres
by
2.7k points

1 Answer

17 votes
17 votes

The equation of a line can be written using the slope-intercept form given as


y=mx+c

For that equation, we need to find m (rate of change) and c (y-intercept).

To find m, we can use the formula


m=(y_2-y_1)/(x_2-x_1)

Let us pick any two points on the graph such that


\begin{gathered} (x_1,y_1)\Rightarrow(-2,10.0) \\ \text{and} \\ (x_2,y_2)\Rightarrow(1,2.5) \end{gathered}

Substituting these into the equation, we have


\begin{gathered} m=(2.5-10.0)/(1-(-2)) \\ m=-(5)/(2) \end{gathered}

The intercept, c, can be calculated by substituting the rate of change, m, and any point coordinates to the equation of a line.

Let us pick the point


(x,y)=(0,5.0)

Substituting, we have


\begin{gathered} 5=(-(5)/(2)*0)+c \\ \therefore \\ c=5 \end{gathered}

Therefore, we have the equation of the line to be


y=-(5)/(2)x+5

Multiplying all terms by 2 to clear out the fraction, we get the equation to be


2y=-5x+10

User Marj
by
2.9k points
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