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Sagot :
We have two points of the line, and we have to find the equation of the line in the slope-intercept form:
[tex]y=mx+b[/tex]First, we find the slope as:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{9-3}{4-1}=\frac{6}{3}=2[/tex]With the value of the slope, we can calculate b replacing the values of x and y with one of the know points:
[tex]\begin{gathered} y=mx+b \\ y=2x+b \\ 3=2\cdot1+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]Now, we have the two parameters (slope and y-intercept) to define the line, and we can write the equation as:
[tex]y=2x+1[/tex]
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