Question

Select the equation of a line that is parallel to the function graphed below:

Answer 1

To find the equation of a line that is parallel to the graph of the given function, we need to determine the slope of the given function.

Looking at the graph of the given function, we can see that it is a straight line with a positive slope. Therefore, the slope of the given function is positive.

To find the equation of a line that is parallel to this function, we need to choose any point on the given line and use the slope to write the equation of the new line.

Let's choose the point (2, 4) on the given line.

Since the slope of the given line is positive, let's choose a slope of 3 for the new line.

Using the point-slope form of a linear equation, the equation of the new line parallel to the given function is:

y - y1 = m(x - x1)

where (x1, y1) is the chosen point on the given line, and m is the slope.

Plugging in the values, we have:

y - 4 = 3(x - 2)