The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.
For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.
To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)
So, using the point (1,-3) and the slope (4), we can write the equation as:
y - (-3) = 4(x - 1)
Simplifying this equation gives:
y + 3 = 4x - 4
Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:
y = 4x - 1
So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1