Question

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

Explanation:

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

Substitute \( x = 0 \) into \( y=\frac{2}{3}x + 1 \).
\( y=\frac{2}{3}(0)+1 = 1 \). So y-intercept is 1.

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

Substitute \( y = 0 \) into \( y=\frac{2}{3}x + 1 \).
\( 0=\frac{2}{3}x + 1 \).
Subtract 1: \( -1=\frac{2}{3}x \).
Multiply by \( \frac{3}{2} \): \( x=-1\times\frac{3}{2}=-\frac{3}{2}=-1\frac{1}{2} \).

Answer:

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