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How do you write an equation of a line with point (5,-2), (7,1)?

Answer 1

Ethan Adkins

#y=3/2x-19/2#

Find slope first: #(y_2-y_1)/(x_2-x_1)# Let's have point 1 as (#5,-2#) and point 2 as (#7,1#)

points are #(x,y)# format, so in #(5,-2)#, #x_1 = 5# and #y_1=-2# and in #(7,1)#, #x_2=7# and #y_2=1#

Therefore the solution will be like this:

Thus, slope #m# is: #(1-(-2))/(7-5)# Simplifying, #(1+2)/(7-5)=3/2#

Let's use point-slope formula, #y-y_1=m(x-x_1)# Adding in values, #y-(-2)=3/2(x-5)#

Now simplify and you get your equation. Make sure to isolate #y#

#y+2=3/2x-15/2# #y=3/2x-15/2-2\rArr3/2x-15/2-2# #\rArry=3/2x-19/2#

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Answer 2

Eva Abramson

To write the equation of a line with two given points (5, -2) and (7, 1), you first find the slope using the formula: ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ), where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points. Then, you choose one of the points and plug its coordinates along with the slope into the point-slope form equation: ( y - y_1 = m(x - x_1) ). Finally, you simplify the equation to slope-intercept form ((y = mx + b)) if necessary.

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Answer from HIX Tutor

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