Chapter 4.4, Problem 9CYU

To determine

To find: The equation of the straight line in slope-intercept form which passes through the point $\left(2,3\right)$ and is perpendicular to the graph of line $2x+3y=4$ .

Answer to Problem 9CYU

Equation of line is $y=\frac{3}{2}x$ having y-intercept 0.

Explanation of Solution

Given information: The given line is $2x+3y=4$ . And, another line is perpendicular to this line which passes through the point $\left(2,3\right)$ .

Concept used: If a line is perpendicular to another line then the slope of that line will be negative reciprocal.

Calculation: Slope $\left(m\right)$ of the line perpendicular to line $2x+3y=4$ , will be $\left(m=\frac{3}{2}\right)$ .

Now, equation of line passing through the point $\left(2,3\right)$ using point-slope form perpendicular to line $2x+3y=4$ is evaluated as,

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\mathrm{......}\left(\text{Using point-slope form}\right)\\ y-3=\frac{3}{2}\left(x-2\right)\mathrm{......}\left(\begin{array}{l}\text{Here, }m=\frac{3}{2}\text{ and}\\ \left(x_1,y_1\right)\to \left(2,3\right)\end{array}\right)\\ y-3=\frac{3}{2}x-3\\ \text{or, }y=\frac{3}{2}x\mathrm{......}\left(\begin{array}{l}\text{Slope-intercept form}\\ \text{having y-intercept 0}\end{array}\right)\end{array}$