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Sagot :
The equation of a straight line given two points (4, -1) and (-8, -7) can be found using the formula:
[tex]\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \text{where the points are:} \\ (x_1,y_1)=(4,-1) \\ (x_2,y_2)=(-8,-7) \end{gathered}[/tex]Put the coordinate points into the formula,
[tex]\begin{gathered} \frac{-7-(-1)}{-8-4}=\frac{y-(-1)}{x-4} \\ \frac{-7+1}{-12}=\frac{y+1}{x-4} \\ \frac{-6}{-12}=\frac{y+1}{x-4} \\ \text{simplify the fraction} \\ \frac{1}{2}=\frac{y+1}{x-4} \\ \text{cross multiply,} \\ 2(y+1)=x-4 \\ \text{divide through by 2,} \\ \frac{2(y+1)}{2}=\frac{x-4}{2} \\ y+1=\frac{x}{2}-\frac{4}{2} \\ \text{simplify the fraction} \\ y+1=\frac{1}{2}x-2 \\ \text{collect like terms} \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Comparing the equation of the line obtained with the formula y = mx + b:
[tex]\begin{gathered} y=mx+c \\ y=\frac{1}{2}x-3 \\ On\text{ comparing,} \\ m=\frac{1}{2} \\ c=-3 \end{gathered}[/tex]Therefore, m= 1/2, c = -3
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