Answer:
y = 4x/3 + 16
Explanation:
Since the point new line is parallel to the line 4x - 3y = 5, so it must have the same slope. We now write this equation in slope-intercept form
4x - 3y = 5
-3y = -4x + 5
y = 4x/3 - 5/3
Its slope is the coefficient of x. So, its slope is 4/3 which will be the slope of the new parallel line which passes through the point (-6, 8).
To find the equation of this line, we use
(y - y₀)/(x - x₀) = m where x₀, y₀ are the points which the line passes through and m = slope of line. Given that ( x₀, y₀) = (-6, 8) and m = 4/3, we substitute these values into the equation. We have
(y - y₀)/(x - x₀) = m
(y - 8)/(x - (-6)) = 4/3
(y - 8)/(x + 6) = 4/3
cross-multiplying, we have
3(y - 8) = 4(x + 6)
Expanding the brackets, we have
3y - 24 = 4x + 24
collecting like terms, we have
3y = 4x + 24 + 24
3y = 4x + 48
In slope-intercept form, it is
y = 4x/3 + 48/3
y = 4x/3 + 16