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Sagot :
Given the points ( 8 , 5 ) and ( 4 , 4 )
The general slop-intercept form of the equation of the line is:
y = mx + c
where m is the slope and c is y-intercept
The slope will be calculated as following:
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{5-4}{8-4}=\frac{1}{4}[/tex]So, the equation of the line will be:
[tex]y=\frac{1}{4}x+c[/tex]Using the one of the given points to find the value of c
Let , we will use the point ( 4 , 4 )
so, when x = 4 , y = 4
[tex]\begin{gathered} 4=\frac{1}{4}\cdot4+c \\ 4=1+c \\ c=4-1=3 \end{gathered}[/tex]So, the slope - intercept equation of the line is:
[tex]y=\frac{1}{4}x+3[/tex]
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