Question

Find the equation of a line, which has the y intercept 4, and is parallel to the line $2x-3y=7$. Find the co-ordinates of the point, where it cuts the x-axis.

• A. $(6,0)$
• B. $(-6,0)$
• C. $(-8,0)$
• D. None of these

Answer 1

The correct option is B $(-6,0)$

The given line $2x-3y=7$ that can be rearranged in to y.

that is $3y=2x-7$

$y=\frac{2}{3}x-7$

the equation has gradient $\frac{2}{3}$ and point $(0,4)$. It can be substitute in the given equation

$y-4=\frac{2}{3}\times (x-0)$

$3y-12=2x$ or $3y=2x+12$

It can cross the x axis when $y=0$

then, $-12=2x$

$x=-6$

we got $x=-6$ and $y=0$ then coordinates of point cut at $(-6,0)$