The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))
Where color(blue)(m) is the slope and (color(red)(x_1, y_1)) is a point the line passes through.
Substituting the slope and values from the point in the problem gives:
(y - color(red)(5)) = color(blue)(-1)(x - color(red)(1))
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)(5) = (color(blue)(-1) xx x) - (color(blue)(-1) xx color(red)(1))
y - color(red)(5) = -1x - (-1)
y - color(red)(5) = -1x + 1
y - color(red)(5) + 5 = -1x + 1 + 5
y - 0 = -1x + 6
y = color(red)(-1)x + color(blue)(6)
