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Q41.

Expert-verified
Found in: Page 66

Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.$41.3x-4y-10=0$

The x-intercept of the given equation is $\frac{10}{3}$ and the y-intercept is $-\frac{5}{2}.$

See the step by step solution

Step 1- Given information

A linear equation $3x-4y-10=0$.

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,

$\begin{array}{l}3x-4y-10=0\\ ⇒3x-4y=10\left(1\right)\end{array}$

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

$\begin{array}{l}3x-4×0=10\\ ⇒3x=10\\ ⇒x=\frac{10}{3}\end{array}$

Therefore, the x-intercept is $\frac{10}{3}$ and the coordinate is

$\left(\frac{10}{3},0\right).$

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

$\begin{array}{l}3×0-4y=10\\ ⇒-4y=10\\ ⇒y=-\frac{5}{2}\end{array}$

Therefore, the y-intercept is $-\frac{5}{2}$ and coordinate is $\left(0,-\frac{5}{2}\right).$

Step 4- Graph of the of the given equation

The graph of the given equation is: