How do you write out the equation of the line passing through #(1,5) (6,15)#?
2 Answers
Explanation:
Use point-slope and slope formula.
We first need to find the slope by finding the change in y over the change in x. This would be
Now if we look at point slope formula, it is
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Explanation:
Apply slope formula
- use formula
#m=(y_2-y_1)/(x_2-x_1)# given two points#(x_1,y_1)# and#(x_2,y_2)# (doesn't matter which one comes first)
the slope you get should be#\color(olive)(m)=10/5=2/1=\color(olive)(2)#
Apply point-slope formula
- now plug-in one of the points for the formula
#y-y_1=m(x-x_1)# ,
which will now become#y-y_1=\color(olive)(2)(x-x_1)# .
here,#\color(indianred){(x_1,y_1)}# can be either of the points.
for easier explanation, used#\color(indianred){(1,5)}#
Working it out
step A
step B
step C
step D
- therefore the equation is:
#\color{cornflowerblue}{y=2x+3}#