First, we need to determine the slope of the line. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.
Substituting the values from the points in the problem gives:
m = (color(red)(-6) - color(blue)(-1))/(color(red)(-2) - color(blue)(1)) = (color(red)(-6) + color(blue)(1))/(color(red)(-2) - color(blue)(1)) = (-5)/(-3) = 5/3m=−6−−1−2−1=−6+1−2−1=−5−3=53
Now, we can use the point-slope formula to write an equation for the line passing through the two points. The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))(y−y1)=m(x−x1)
Where color(blue)(m)m is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
Substituting the slope we calculated and the first point gives:
(y - color(red)(-1)) = color(blue)(5/3)(x - color(red)(1))
(y + color(red)(1)) = color(blue)(5/3)(x - color(red)(1))
We can also substitute the slope we calculated and the second point giving:
(y - color(red)(-6)) = color(blue)(5/3)(x - color(red)(-2))
(y + color(red)(6)) = color(blue)(5/3)(x + color(red)(2))
We can also solve this equation for y to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: y = color(red)(m)x + color(blue)(b)
Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.
y + color(red)(6) = (color(blue)(5/3) xx x) + (color(blue)(5/3) xx color(red)(2))
y + color(red)(6) = 5/3x + 10/3
y + color(red)(6) - 6 = 5/3x + 10/3 - 6
y + 0 = 5/3x + 10/3 - (3/3 xx 6)
y = 5/3x + 10/3 - 18/3
y = color(red)(5/3)x - color(blue)(8/3)
