Question

Which of the following is the equation of given line joining point A and point B?

• A. $3y=2x+5$
• B. $2y=3x+5$
• C. $3y+2x=5$
• D. $2y+3x=5$

Answer 1

The correct option is A $3y=2x+5$

We can see coordinates of pt.A and pt. B in the graph,
$A(2,3),B(-1,1)$

$\text{Slope}=\frac{\text{rate of change of y}}{\text{rate of change of x}}$

Slope of the line $=\frac{3-1}{2-(-1)}=\frac{2}{3}$

Slope-intercept form of the line is $y=\frac{2}{3}x+b$
where $b$ is y-intercept form of line.

We find the value of $b$ by substituting value of $x\&y$ in the equation of line:
$3=\frac{2}{3}\times 2+b\Rightarrow 3=\frac{4}{3}+b\Rightarrow b=\frac{5}{3}$

Hence, equation of the line is $y=\frac{2}{3}x+\frac{5}{3}$