18) through: (5,4) parallel to y=(3)/(5)x-1 A) y=(3)/(5)x+1 B) y=-(3)/(5)x+1 C) y=(2)/(5)x-(3)/(5) D) y=x-(3)/(5)

To find the equation of the line that passes through the point $(5,4)$ and is parallel to the line $y=\frac{3}{5}x-1$, we need to use the fact that parallel lines have the same slope.<br /><br />The slope of the given line $y=\frac{3}{5}x-1$ is $\frac{3}{5}$. Since the line we are looking for is parallel to this line, it will also have a slope of $\frac{3}{5}$.<br /><br />Now, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:<br /><br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope.<br /><br />Substituting the given point $(5,4)$ and the slope $\frac{3}{5}$ into the point-slope form, we get:<br /><br />$y - 4 = \frac{3}{5}(x - 5)$<br /><br />Simplifying this equation, we have:<br /><br />$y - 4 = \frac{3}{5}x - 3$<br /><br />$y = \frac{3}{5}x + 1$<br /><br />Therefore, the equation of the line that passes through the point $(5,4)$ and is parallel to the line $y=\frac{3}{5}x-1$ is $y=\frac{3}{5}x+1$.<br /><br />So, the correct answer is A) $y=\frac{3}{5}x+1$.