Use the image to answer the question.

Question

A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.

Is the point (1/2,−1 1/2)
a solution to the inequality y>4/5x−3
, as shown on the graph? Enter 1 for yes or 2 for no.

(1 point)

Answer 1

To determine whether the point \((\frac{1}{2}, -\frac{3}{2})\) is a solution to the inequality \(y > \frac{4}{5}x - 3\), we need to check if the coordinates of the point satisfy the inequality.

1. Substitute \(x = \frac{1}{2}\) into the equation of the line: \[ y = \frac{4}{5}\left(\frac{1}{2}\right) - 3 \] Calculating this, we have: \[ y = \frac{4}{10} - 3 = \frac{2}{5} - 3 = \frac{2}{5} - \frac{15}{5} = -\frac{13}{5} = -2.6 \]

2. Now, we check if \(y > -2.6\) when \(y = -\frac{3}{2} = -1.5\): \[ -1.5 > -2.6 \] This statement is true.

Since the point \((\frac{1}{2}, -\frac{3}{2})\) does satisfy the inequality \(y > \frac{4}{5}x - 3\):

The answer is 1 for yes.