Question

Select the equation that is parallel to y = x+4 and goes through (2,2)

a
y=x+2

b
y=x

c
y=x-4

Answer 1

To find the equation of a line that is parallel to \( y = x + 4 \) and goes through the point \( (2, 2) \), we need to observe that parallel lines have the same slope. The slope of the given line \( y = x + 4 \) is \( 1 \).

Since the slope must remain the same, the equation of the line we are looking for will also have a slope of \( 1 \). We can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

Here, \( (x_1, y_1) = (2, 2) \) and \( m = 1 \):

\[
y - 2 = 1(x - 2)
\]

Simplifying this, we get:

\[
y - 2 = x - 2
\]

\[
y = x
\]

Now, let's analyze the options provided:

a) \( y = x + 2 \)

b) \( y = x \)

c) \( y = x - 4 \)

The equation that matches what we obtained is:

**b) \( y = x \)**

So, the correct answer is **b**.