We can use the point-slope formula to find the equation of the line. 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)(-6)) = color(blue)(1)(x - color(red)(4))
(y + color(red)(6)) = color(blue)(1)(x - color(red)(4))
If necessary, we can convert this equation to slope-intercept by solving for y. 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) = x - color(red)(4)
y + color(red)(6) - 6 = x - color(red)(4) - 6
y + 0 = x - 10
y = color(red)(1)x - color(blue)(10)
