To write an equation for this line give the slope and one point use the point-slope formula.
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 point and slope from the problem gives:
(y - color(red)(5)) = color(blue)(-2/5)(x - color(red)(-8))
(y - color(red)(5)) = color(blue)(-2/5)(x + color(red)(8))
Or, we can solve for y to put this equation in the more familiar 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)(-2/5)x + (color(blue)(-2/5) xx color(red)(8))
y - color(red)(5) = color(blue)(-2/5)x - 16/5
y - color(red)(5) + 5 = color(blue)(-2/5)x - 16/5 + 5
y - 0 = -2/5x - 16/5 + (5/5 xx 5)
y = -2/5x - 16/5 + 25/5
y = -2/5x + 9/5
