Write an equation in slope-intercept form of the line that passes through (6,-2) and (12,1)

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 formLearn more about equation of line at:brainly.com/question/4361464brainly.com/question/4390083#LearnwithBrainly