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Sagot :
Given the set of values, you have to determine the y-intercept, slope, and the equation that corresponds to de relationship on the table.
The slope-intercept form is
[tex]y=mx+b[/tex]Where
m represents the slope
b represents the y-intercept (is the y-coordinate of the point corresponding to the y-intercept)
The y-intercept of any function in the coordinate system is the point where the line intercepts the y-axis, at this point the x-coordinate is equal to zero. You can determine this value directly from the table, the ordered pair (0,6) corresponds to the y-intercept coordinates.
So "b = 6"
To determine the slope of the line, m, you need to use two points of the line and the following formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]Where
(x₁,y₁) are the coordinates of one point on the line
(x₂,y₂) are the coordinates of a second point on the line
You can use any two points of the line to calculate the slope, I will use (2,14) and (1,10)
[tex]\begin{gathered} m=\frac{14-10}{2-1} \\ m=\frac{4}{1} \\ m=4 \end{gathered}[/tex]The slope of the line is m=4
Finally, you have to replace the values of the slope and y-intercept in the formula to determine the equation of the line in slope-intercept form:
[tex]y=mx+b[/tex]For b=6 and m=4
[tex]y=4x+6[/tex]
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