How do you write the equation for a line that passes through points (2,1) and (0,7)?

1 Answer
smendyka
Dec 14, 2016

#y - 7 = -3x# or #y = -3x + 7#

Explanation:

To find the equation of a line passing through two points you must first find the slope of the line.

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. Substituting the two points give in the problem allows us to calculate the slope as:

#m = (7 - 1)/(0 - 2)#

#m = 6/(-2)#

#m = -3#

Next we can use the point-slope formula to find the equation for the line passing through these two points.

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

We can substitute #-3# for me and (0, 7) for the point giving:

#y - 7 = -3(x - 0)#

#y - 7 = -3x - 3*0#

#y - 7 = -3x#

Solving for the slope intercept form gives:

#y - 7 + 7 = -3x + 7#

#y - 0 = -3x + 7#

#y = -3x + 7#

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