To find the intersection of the graphs of the equations \( y = 4x^2 - 5x + 3 \) and \( y = 3x \), you need to set the two equations equal to each other because at the points of intersection, the \( y \) values will be the same.
This leads us to the equation:
\[ 4x^2 - 5x + 3 = 3x \]
To solve it, you can rearrange it to bring all terms to one side of the equation:
\[ 4x^2 - 5x + 3 - 3x = 0 \]
This simplifies to:
\[ 4x^2 - 8x + 3 = 0 \]
Therefore, the correct choice from your responses to find the intersection is:
\[ 4x^2 - 5x + 3 = 3 \]
However, this could also be written as \( 3x = 4x^2 - 5x + 3 \) by rearranging the terms. So both \( 4x^2 - 5x + 3 = 3 \) and \( 3x = 4x^2 - 5x + 3 \) could also be considered valid equations depending on how you want to set it up.
The simplest choice from your options is:
\[ 4x^2 - 5x + 3 = 3 \]
2 answers