Answer:
[tex]y = \frac{3x}{2}+1[/tex]
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 [tex]y = -\frac{2x}{3} +6[/tex] will be [tex]y= \frac{3x}{2}+ c'[/tex] ....... (1), where c' is constant.
Given that the line (1) passes through (2,4) point.
Hence, [tex]4 = \frac{3(2)}{2} +c'[/tex]
⇒ c' = 1.
Therefore, the final equation of the required straight line is [tex]y = \frac{3x}{2}+1[/tex]. (Answer)
