Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form? y = x + 8 y = x − 8 y = −5x − 10 y = −5x + 20

Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form.

y = x + 8
y = x − 8
y = −5x − 10
y = −5x + 20

2 Answers
Micu
Jun 23, 2018

#y=x+8#

Explanation:

The general equation of a line is y=mx+n, where m is the slope, and n is the Y intercept.
We know that the two points are situated on this line, and therefore verify it's equation.
#5=-3m+n#
#10=2m+n#
We can treat the two equations as a system and can subtract the first equation from the first giving us:
#5=5m => m=1#
Now we can plug #m# into any of our initial equations to find #n#
For example:
#5=-3+n => n=8#
Final answer:
#y=x+8#

Jim G.
Jun 23, 2018

#y=x+8#

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)=(-3,5)" and "(x_2,y_2)=(2,10)#

#m=(10-5)/(2-(-3))=5/5=1#

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

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

#"using "(2,10)" then"#

#10=2+brArrb=10-2=8#

#y=x+8larrcolor(red)"in slope-intercept form"#

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