Question

what is the equation in slope intercept form of the line that goes through (2,4) and is perpendicular to the line represented by y=-2/3x+6

Answer 1

Answer:

$y = \frac{3x}{2}+1$

Step-by-step explanation:

The slope-intercept form of a straight line equation is y = mx + c, where m is the slope and c is the y-intercept of the line.

Now, we know that if two straight lines are perpendicular to each other then the product of their slopes will be -1.

So, the equation of a straight line which is perpendicular to the line $y = -\frac{2x}{3} +6$ will be $y= \frac{3x}{2}+ c'$ ....... (1), where c' is constant.

Given that the line (1) passes through (2,4) point.

Hence, $4 = \frac{3(2)}{2} +c'$

⇒ c' = 1.  

Therefore, the final equation of the required straight line is $y = \frac{3x}{2}+1$. (Answer)