Question

find the x-intercept and y-intercept of the graph of the equation $2x - 3y = 5$.\
\
\\(\bigcirc\\) a) x-intercept: $2\frac{1}{2}$\
\quad\quad\quad y-intercept: $-1\frac{2}{3}$\
\
\\(\bigcirc\\) b) x-intercept: $2\frac{1}{2}$\
\quad\quad\quad y-intercept: $-5$\
\
\\(\bigcirc\\) c) x-intercept: $2\frac{1}{2}$\
\quad\quad\quad y-intercept: $1\frac{2}{3}$\
\
\\(\bigcirc\\) d) x-intercept: $2$\
\quad\quad\quad y-intercept: $-3$

Explanation:

Step1: Find x-intercept (set y=0)

Substitute \( y = 0 \) into \( 2x - 3y = 5 \):
\( 2x - 3(0) = 5 \)
\( 2x = 5 \)
\( x = \frac{5}{2} = 2\frac{1}{2} \)

Step2: Find y-intercept (set x=0)

Substitute \( x = 0 \) into \( 2x - 3y = 5 \):
\( 2(0) - 3y = 5 \)
\( -3y = 5 \)
\( y = -\frac{5}{3} = -1\frac{2}{3} \)

Answer:

A) x-intercept: \( 2\frac{1}{2} \), y-intercept: \( -1\frac{2}{3} \)