Parallel lines refers to a pair of straight lines that never intercept or touch each other. The slopes of this lines is the same one.
On this exercise is given the equation of a line and a point, and is asked to find the equation of a line in slope-intercept form that is parallel to the given one, and that passes through the given point.
y-1=4(x+3) Distribute the parenthesis
y-1=4x+12 Add 1 in both sides to isolate y
y=4x+13
The slope of the given line is 4, which means that the slope of a line parallel to this one, have to be 4. Now you need to find the value of b or the y-intercept by substituting the given point into the slope-intercept form y=mx+b, where the letter m represents the slope.
y=mx+b Substitute the values of the given point and slope
32=4(4)+b Combine like terms
32=16+b Subtract 16 in both sides to isolate b
16=b
The equation is slope-intercept form for the line that passes through the point (4,32) and is parallel to the given line is y=4x+16.