What is the equation of the line that passes through the points (2, 4) and (4,0)?

2 Answers
Nov 9, 2016

#y=-2x+8#

Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
where m represents the slope and b, the y-intercept

We require to find m and b to establish the equation.

To find 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)" and " (x_2,y_2)" are 2 coordinate points"#

The 2 points here are (2 ,4) and (4 ,0)

let # (x_1,y_1)=(2,4)" and " (x_2,y_2)=(4,0)#

#rArrm=(0-4)/(4-2)=(-4)/2=-2#

We can write the partial equation as #y=-2x+b#

To find b, substitute either of the 2 points into the partial equation and solve for b.

Using (4 ,0), that is x = 4 and y = 0

#rArr0=(-2xx4)+brArr0=-8+brArrb=8#

#rArry=-2x+8" is the equation"#

Nov 9, 2016

#2x+y=8#

Explanation:

If two coordinates are known a more direct formula is;

#(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)#

#(x_1,y_1)=(2,4)#

#(x_2,y_2)=(4,0)#

#(y-4)/(0-4)=(x-2)/(4-2#

#y/-4=(x-4)/2#

#2y=-4x+8#

#4x+2y=16#

#2x+y=8#