How do you write an equation of a line through: (2,4) and (5,1)?

1 Answer
smendyka
Dec 17, 2016

y - 4 = -1(x - 2)y−4=−1(x−2) or y = -x + 6y=−x+6

Explanation:

To write this equation we can use the point-slope formula. To use this formula we must first determine the slope.

The slope can be found by using the formula: color(red)(m = (y_2 = y_1)/(x_2 - x_1)m=y2=y1x2−x1
Where mm is the slope and (x_1, y_1)(x1,y1) and (x_2, y_2)(x2,y2) are the two points.

Using the two points given in the problem the slope is:

m = (1 - 4)/(5 - 2)m=1−45−2

m = -3/3m=−33

m = -1m=−1

Now we can use the point-slope formula to determine the equation:

The point-slope formula states: color(red)((y - y_1) = m(x - x_1))(y−y1)=m(x−x1)
Where mm is the slope and #(x_1, y_1) is a point the line passes through.

Using the slope we calculate and one of the points gives:

y - 4 = -1(x - 2)y−4=−1(x−2)

Solving for yy to put this equation into the slope-intercept form gives:

y - 4 = -x + 2y−4=−x+2

y - 4 + 4 = -x + 2 + 4y−4+4=−x+2+4

y - 0 = -x + 6y−0=−x+6

y = -x + 6y=−x+6

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