What is the equation of the line passing through (24,18)(24,18) and (9,12)(9,12)?

2 Answers
Jim G.
Jun 8, 2018

y=2/5x+42/5y=25x+425

Explanation:

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

•color(white)(x)y=mx+b∙xy=mx+b

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)∙xm=y2−y1x2−x1

"let "(x_1,y_1)=(24,18)" and "(x_2,y_2)=(9,12)let (x1,y1)=(24,18) and (x2,y2)=(9,12)

m=(12-18)/(9-24)=(-6)/(-15)=2/5m=12−189−24=−6−15=25

y=2/5x+blarrcolor(blue)"is the partial equation"y=25x+b←is the partial equation

"to find b substitute either of the 2 given points into"to find b substitute either of the 2 given points into
"the partial equation"the partial equation

"using "(9,12)" then"using (9,12) then

12=18/5+brArrb=60/5-18/5=42/512=185+b⇒b=605−185=425

y=2/5x+42/5larrcolor(red)"is equation of line"y=25x+425←is equation of line

Sonnhard
Jun 8, 2018

y=2/5*x+42/5y=25⋅x+425

Explanation:

We get the slope as
m=(y_2-y_1)/(x_2-x_1)=(12-18)/(9-24)=2/5m=y2−y1x2−x1=12−189−24=25
so we have
y=2/5x+ny=25x+n
using
x=9,y=12x=9,y=12
we get
n=42/5n=425

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