We can use the point-slope formula to find this equation. 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 values from the problem gives:
(y - color(red)(-6)) = color(blue)(-1)(x - color(red)(1))
(y + color(red)(6)) = color(blue)(-1)(x - color(red)(1))
Or we can solve 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)(-1) xx x) - (color(blue)(-1) xx color(red)(1))
y + color(red)(6) = -x + 1
y + color(red)(6) - 6 = -x + 1 - 6
y + 0 = -x - 5
y = color(red)(-1)x - color(blue)(5)
