Find the equation of a line that is parallel to y=3x+5 that goes through point (4,7).Use parentheses around a fraction in your answer.

Answer 1

1) To answer this question, you first have to quickly understand one thing. Parallel lines will have the same slope but different y intercepts. If you don't understand this, draw a line on a piece of graph paper. Then draw another line adjacent to it. If the slope is different, the two lines will intersect as you extend the lines out indefinitely.

2) Ok, now let us look at point 1 above and see how that helps us with our problem. The equation we are given is this:

y = 3x+5

To understand what this equation is all about, we need to understand the general equation of a line.

A line has this equation:

y = mx + b --> In the equation of a line in this format, m is the slope and b is the y-intercept.

If we look at our equation y=3x+5, you will notice that m is 3 and b is 5. Therefore, we now know that 3 is the slope of the line and 5 is where the line intersects the y-axis.

3) So based on what we discussed in point 1 above, we know that the new parallel line will have m=3 because it will have the same slope. Only the y-intercept will change for the new line.

Therefore, the equation of the new line will have this format:

y = 3x + b

Notice here that we substituted 3 in the place of m and left b alone because we don't know what b is yet.

Now if we go back to our question, we are given one more piece of information to figure b out. The question tells us that the new parallel line goes through the point (4,7).

Let us translate what this means to better understand it. It means that the new parallel line will have a y-value of 7 when x is 4.

4) Now using what we learned so far, let us solve the equation. We know that the new line will have the form:

y=3x+b

We know that when x is 4, y will be 7 because the question tells us this. Let us substitute these values and solve for b.

7 = 3(4) + b

7 = 12 + b

subtract 12 from both sides:

7-12 = b + 12 - 12

-5 = b

or rewritten as

b = -5

5) Great now we know what m is and what b is. m=3 and b = -5

The equation of the new line and the answer to our question therefore will be :

y = mx+b

y = 3x - 5

Answer 2

Parallel lines have the same slope. The slope ("m") of the first line is 3. So, m=3 and x₁=4 and y₁= 7. Using point-slope form (y-y₁ = m (x-x₁)) you have

y-7=3(x-4)

y-7=3x-12

y=3x-5

Answer 3

slope of the line = 3 = the coefficient of the x term

slope also = (y-7)/(x-4) = 3

3x -12 = y-7

y = 3x -12+7

y = 3x -5 is the equation of the line parallel to the given equation through the given point