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Q42.

Expert-verified

Algebra 2

Found in: Page 66

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.
$2 x + 5 y - 10 = 0$

The x-intercept of the given equation is $5$ and the y-intercept is $2 .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1- Given information

A linear equation $2 x + 5 y - 10 = 0$ .

Step 2- Concept used

The y-coordinate of the point at which a graph crosses the y-axis is called the y-intercept.

So, the y-intercept is the value of $y$ when $x = 0 .$

The x-coordinate of the point at which a graph crosses the x-axis is called the x-intercept.

So, the x-intercept is the value of $x$ when $y = 0 .$

Step 3- To find the x-intercept and y-intercept.

From the given information,

$\begin{array}{l} 2 x + 5 y - 10 = 0 \\ \Rightarrow 2 x + 5 y = 10 . . . . . . (1) \end{array}$

Substitute the $y = 0$ in the equation (1).

$\begin{array}{l} 2 x + 5 \times 0 = 10 \\ \Rightarrow 2 x = 10 \\ \Rightarrow x = 5 \end{array}$

Therefore, the x-intercept is $5$ and the coordinate is

$(5, 0) .$

Now, substitute the $x = 0$ in the given equation (1).

$\begin{array}{l} 2 \times 0 + 5 y = 10 \\ \Rightarrow 5 y = 10 \\ \Rightarrow y = 2 \end{array}$

Therefore, the y-intercept is $2$ and coordinate is $(0, 2) .$

Step 4- Graph of the of the given equation

The graph of the given equation is:

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