Write an equation for a line that is parallel to the given line that passes through the given point. explain how you found the equation. y=2x+7; (3,11) show all work plz

Slope-intercept form:

y = mx + b   "m" is the slope, "b" is the y-intercept (the y value when x = 0)

For lines to be parallel, they have to have the SAME slope.

The given line's slope is 2, so the parallel line's slope is also 2.

y = 2x + b

To find "b", plug in the point (3,11) into the equation.

y = 2x + b

11 = 2(3) + b      Multiply 2 and 3

11 = 6 + b      Subtract 6 on both sides

5 = b

y = 2x + 5

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2