Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Mixed Review - Page 484: 53


$y \geq \frac{4}{5}x - 2$

Work Step by Step

$4x - 5y \geq 10$ Subtract $4x$ from both sides to isolate $-5y$. $-5y \geq -4x + 10$ Divide both sides by $-5$ to simplify the inequality. $y \geq \frac{4}{5}x - 2$ The inequality is now in slope-intercept form ($y = mx + b$), where $m$ represents the slope and $b$ represents the y-intercept. The slope is $\frac{4}{5}$; the y-intercept is $-2$. A solid line is used for inequalities with $\geq$ or $\leq$ as each point on the line is a solution. If the inequality has $\gt$ or $\lt$, a dashed line is used since solutions cannot be equal to any point on the line. One side of the graph divided by the line is shaded to represent the points included in the solution. To determine which side to shade, test a point that is not on the line. We will use $(0, 0)$ for example. Substitute the values of the point for $(x, y)$ and simplify. $0 \geq \frac{4}{5}(0) - 2$ $0 \geq -2$ The inequality is true with the values $(0, 0)$. If a point is a solution for an inequality, so are all the others on the same side of the boundary line. $(0, 0)$ is above the line, so the area above is shaded.
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