How do you write the equation of the line parallel to y = 3x - 4 and passing through the point (-2, 5)?

Answer 1

#y =3x+11#

Parallel lines have the same slopes.

The slope of the new line will have the same slope as the given line:

#y = color(red)(3)x -4 rArr m= color(red)(3)#
One point on the line is given, #color(blue)(((-2, 5))). "This is " color(blue)(((x_1, y_1)))#
The formula for slope is #m = ("change in y values"/"change in x-values") = (y_2-y_1)/(x_2-x_1)#

If you have the slope and one point , substitute them into a formula which is based on the formula for slope given above.

#y-color(blue)(y_1) = color(red)(m)(x-color(blue)(x_1))#
#y-color(blue)(5) = color(red)(3)(x-color(blue)((-2)))# #y-5 =3(x+2)#

Simplify to get the required equation of the line.

#y = 3x+6+5#
#y =3x+11#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To write the equation of a line parallel to y = 3x - 4 and passing through the point (-2, 5), we use the fact that parallel lines have the same slope. The slope of the line y = 3x - 4 is 3. So, the slope of the parallel line will also be 3. Now, we use the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope. Substituting the values, we get y - 5 = 3(x - (-2)). Simplifying, we get y - 5 = 3(x + 2). Expanding and simplifying further, we get y - 5 = 3x + 6. Finally, we add 5 to both sides to isolate y, yielding y = 3x + 11. Therefore, the equation of the line parallel to y = 3x - 4 and passing through the point (-2, 5) is y = 3x + 11.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7