Question

Line $k$ has a slope of $4/5$ and passes through the point $(1,1)$. Line $l$ is parallel to line $k$ and has a $y$-intercept $3$ times that of line $k$. Which of the following is the equation of line $l$ ?

• A. $5y-4x=3$
• B. $5y-x=4$
• C. $10y-8x=30$
• D. $20y+25x=12$

Answer 1

The correct option is A $5y-4x=3$

The equation of line who slope of $\frac{4}{5}$ and passes though the point is line $k$

$(y-1)=\frac{4}{5}(x-1)$
$\Rightarrow 5y-5=4x-4$

$\Rightarrow 5y-4x=-4+5$

$\Rightarrow 5y-4x=1$

We know that two line are parallel to another line the slop of both line is equal, then $y=mx+c$ (Where $m$ is the slope and $c$ is the intercept point of $y$-axis)

Then line $l$ is slope $\frac{4}{5}$ and $3$ is the intercept point of $y$-axis.

$y=\frac{4}{5}x+3$

$\Rightarrow 5y=4x+3$

$\Rightarrow 5y-4x=3$