Lines and intersect at a point

MATHEMATICS · Single correct · CBSE · Mathematics · Straight Lines · Straight Lines

Problem

Lines

2x+3y-6=0

and

y=x+1

intersect at a point

P

. A new line passes through

P

with slope

-\dfrac{4}{5}

. Which of the following is its equation in slope–intercept form? (a)

y=-\dfrac{4}{5}x+\dfrac{32}{25}

(b)

y=-\dfrac{4}{5}x+\dfrac{52}{25}

(c)

y=\dfrac{4}{5}x+\dfrac{52}{25}

(d)

y=-\dfrac{5}{4}x+\dfrac{52}{25}