1 answer

What is the equation of line that goes through #(-1, -3)# and #(2, 5)#?

Question:

What is the equation of line that goes through #(-1, -3)# and #(2, 5)#?

Answers

#8x -3y = 8" OR " y=8/3x -8/3" OR "8x -3y -8=0#

Explanation:

There are several methods to do this: Use the method you are most comfortable with.

#1.# Find the slope, then use that and one point to find #c#,
Hence get the equation of the line. #y = mx + c#

#2#. Write 2 equations using the given points and solve them simultaneously to find values for #m and c#

#3#. Find the slope and then using that and one point, substitute into the point-slope formula: #y-y_1 = m(x-x_1)#

#4#. Substitute both points into the formula: #(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)#

I will choose to use method 4.

The slope is obtained as part of the working, which is quite useful.

#(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)# with #(-1,-3) and (2,5)#

#(y-(-3))/(x-(-1)) =(5-(-3))/(2-(-1)) = 8/3" " (m= 8/3)#

#(y+3)/(x+1) = 8/3" "larr# now cross multiply

#3(y+3) = 8(x+1)#

#3y +9 = 8x+1" "larr# now decide which form you would like.

#8x -3y = 8" "larr# standard form

# y=8/3x -8/3" "larr# slope-intercept form

#8x -3y -8=0" "larr# general form

.

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