Write an equation of a line whose graph is parallel to the graph of y=3x-10

y = 3x + d, where d can take on any real value.

Step-by-step explanation:

The given equation is y = 3x - 10.  If the new line is to be parallel to this one, then the new line must have the same slope:  m = 3.

Then the general form of this new line would be y = 3x + d, where d can have any real value.

y = 3x  

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts.

Your function has y-intercept b = -10.

Choose any different value for b. How about b = 0?

Then, the equation for the parallel line is

y = 3x

In the diagram below, the red line is the graph of y = 3x – 10.

The parallel blue line is the graph of y = 3x.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b