Question #d8011
1 Answer
Explanation:
The equation of a line in
#color(blue)"point-slope form "# is
#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and#(x_1,y_1)" a point on the line"# 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)|)))#
where# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"# The 2 points here are (0 ,4) and (1 ,7)
let
# (x_1,y_1)=(0,4)" and " (x_2,y_2)=(1,7)#
#rArrm=(7-4)/(1-0)=3/1=3# Either of the 2 points may be used as
# (x_1,y_1)# as both lie on the line.
#"Using "m=3" and " (x_1,y_1)=(1,7)# Substitute these values into the equation.
#y-7=3(x-1)larrcolor(red)" in point-slope form"# distributing and simplifying gives an alternative version of the equation.
#y-7=3x-3rArry=3x-3+7#
#rArry=3x+4larrcolor(red)" in slope-intercept form"#
