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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)?

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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)

Step 1

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

Step 2

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

Step 3

Solve for b (the y-intercept) 

Step 4

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

Method 2: Using Post Slope Form

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!

Step 1

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)

Step 2

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

Practice ProblemsProblem 1 - Method 1

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

Answer:

y = 4x + 16

Step-by-step explanation:

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