Question

Write the equation that is parallel to the below graph and goes through the origin.



a
y=(-3/4)x

b
y=(-1/2)x

c
y=(4/3)x-2

d
y=(4/3)x

Answer 1

To find an equation that is parallel to the given graph \( y = -\frac{3}{4}x \) and goes through the origin, we first need to identify the slope of the given equation. The slope of the line \( y = -\frac{3}{4}x \) is \( -\frac{3}{4} \).

Since parallel lines have the same slope, the equation we want to find will also have a slope of \( -\frac{3}{4} \).

The general form of a line that goes through the origin can be expressed as:

\[
y = mx
\]

where \( m \) is the slope. Thus, substituting the slope we found:

\[
y = -\frac{3}{4}x
\]

Now let's analyze the options provided:

- a. \( y = -\frac{3}{4}x \) (this is the original equation, so it is parallel)
- b. \( y = -\frac{1}{2}x \) (different slope, not parallel)
- c. \( y = \frac{4}{3}x - 2 \) (different slope, not parallel)
- d. \( y = \frac{4}{3}x \) (different slope, not parallel)

The only equation that is parallel to the provided line and goes through the origin is option **a**:

\[
y = -\frac{3}{4}x
\]

It is important to note that if you intended a different original equation, please provide that specific equation.