We can use the point slope formula to write an equation for this 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 the values from the point from the problem gives:
(y - color(red)(3)) = color(blue)(2)(x - color(red)(-4))
Solution 1: (y - color(red)(3)) = color(blue)(2)(x + color(red)(4))
We can also solve for y to put this 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)(3) = (color(blue)(2) xx x) + (color(blue)(2) xx color(red)(4))
y - color(red)(3) = 2x + 8
y - color(red)(3) + 3 = 2x + 8 + 3
y - 0 = 2x + 11
Solution 2: y = color(red)(2)x + color(blue)(11)
