Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:
[tex]y =\frac{1}{2}x-5[/tex]
Step-by-step explanation:
Given points are:
(x1,y1) = (6,-2)
(x2,y2) = (12,1)
The slope intercept form is:
[tex]y=mx+b[/tex]
We have to find the slope first
[tex]m =\frac{y_2-y_1}{x_2-x_1}\\=\frac{1-(-2)}{12-6}\\= \frac{1+2}{6}\\=\frac{3}{6}\\=\frac{1}{2}[/tex]
Putting the value of slope
[tex]y = \frac{1}{2}x+b[/tex]
To find the value of b, putting (12,1) in the equation
[tex]1 = \frac{1}{2}(12)+b\\1 = 6+b\\b = 1-6\\b=-5[/tex]
Putting the values of m and b
[tex]y =\frac{1}{2}x-5[/tex]
Hence,
Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:
[tex]y =\frac{1}{2}x-5[/tex]
Keywords: Equation of line, slope-intercept form
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