What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?

What is the equation of line parallel to y = 3x + 5 and through the point (1, 7)?

Many students are more comfortable using slope intercept form but this kind of problem is actually much easier , using point slope form (which is right below this work)

Substitute the slope from original line (3 in this case) into the equation of the line y = 3x + b

Substitute the given point (1,7) into the x and y values 7 = 3(1) + b

Solve for b (the y-intercept) 

Substitute this value for 'b' in the slope intercept form equation y = 3x + 4

What is the equation of line parallel to y = 3x + 5 and through the point (1, 7)?

If you're comfortable with point slope form , this is the way to go! Just look how little work there is to do! In fact, all that you have to do is substitute twice!

Substitute the slope from original line (3 in this case) into the point slope equation y − y1 = m(x − x1) 
y − y1 = 3(x − x1)

Substitute the given point (1,7) into the x1 and y1 values y − 7= 3(x − 1)

What is the equation of line parallel to y = 4x + 3 and through the point (5,9)?