#"the equation of a line in "color(blue)"point-slope form"# is.

#•color(white)(x)y-y_1=m(x-x_1)#

#"where m is the slope and "(x_1,y_1)" a point on the line"#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"to calculate m use the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(2,7)" and "(x_2,y_2)=(-2,9)#

#rArrm=(9-7)/(-2-2)=2/(-4)=-1/2#

#"to obtain the point-slope equation"#

#"with "m=-1/2" and "(x_1,y_1)=(2,7)#

#y-7=-1/2(x-2)larrcolor(red)"in point-slope form"#

#"rearranging into slope-intercept form"#

#y-7=-1/2x+1#

#rArry=-1/2x+8larrcolor(red)" in slope-intercept form"#