How do you find the equation of the line that passes through the points (7,3) and (2,5)?

1 Answer
smendyka
Dec 15, 2016

#y - 3 = -2/5(x - 7)# or #y = -2/5x + 29/5#

Explanation:

To find the line passing through these two points we will use the point-slope formula. However, first we must determine the slope.

The slope can be found by using the formula: #color(red)(m = (y_2 = y_1)/(x_2 - x_1)#
Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the two points.

For our problem we can substitute and find the slope as:

#m = (5 - 3)/(2 - 7)#

#m = 2/(-5) = -2/5#

Now we can use the point-slope formula. The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))#
Where #m# is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope we calculated and one of the points we were given.

#y - 3 = -2/5(x - 7)#

or, converting to slope-intercept form:

#y - 3 = -2/5x + 14/5#

#y - 3 + 3 = -2/5x + 14/5 + 3#

#y - 0 = -2/5x + 14/5 + 3(5/5)#

#y = -2/5x + 14/5 + 15/5#

#y = -2/5x + 29/5#

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