The slope-intercept form of the line is [tex]y=\dfrac{1}{4}x[/tex].
Given:
A line passes through the two points [tex](4,1)[/tex] and [tex](8,2)[/tex].
To find:
The slope-intercept form of the line.
Explanation:
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]
Where, [tex]m[/tex] is slope and [tex]b[/tex] is the y-intercept.
The line passes through the two points [tex](4,1)[/tex] and [tex](8,2)[/tex]. So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-1=\dfrac{2-1}{8-4}(x-4)[/tex]
[tex]y-1=\dfrac{1}{4}(x-4)[/tex]
Using the distributive property, we get
[tex]y-1=\dfrac{1}{4}(x)+\dfrac{1}{4}(-4)[/tex]
[tex]y=\dfrac{1}{4}x-1+1[/tex]
[tex]y=\dfrac{1}{4}x[/tex]
Therefore, the slope-intercept form of the line is [tex]y=\dfrac{1}{4}x[/tex].
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