# 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"#