What's the equation of a line that passes through (-4,1) and (0,5).?

2 Answers
Jim G.
Apr 7, 2018

#y=x+5#

Explanation:

#"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(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(-4,1)" and "(x_2,y_2)=(0,5)#

#rArrm=(5-1)/(0-(-4))=4/4=1#

#rArry=x+blarrcolor(blue)"is the partial equation"#

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

#"using "(0,5)" then"#

#5=0+brArrb=5#

#rArry=x+5larrcolor(red)"equation in slope-intercept form"#

Yahia M.
Apr 7, 2018

#y+x-5=0#

Explanation:

The formula to get the equation of a straight line knowing two points that lie on it is:
#(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)#

where the two points are #(x_1,y_1)# and#(x_2,y_2)# and you can pick any of the points to be one of them.

And by substituting you get:

#(y-5)/(x-0)=(5-1)/(-4-0)#

And by simplifying you get:
#y-5=-x#
so the equation is #y+x-5=0#

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