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Chapter 2: Q11. (page 65)

Find the x-intercept and the y-intercept of the graph of each equation. Then graph the equation.

3x+2y=6

Short Answer

Expert verified

The x-intercept is 2 and y-intercept is 3. The graph of the equation is:

Step by step solution

01

– Definition of intercepts.

The x-intercept is the point where the graph intersect the x-axis. It is the value of x when y=0.

The y-intercept is the y-intercept is the point where the graph intersect the x-axis. It is the value of y when x=0.

02

– Find the x-intercept.

The given equation is:

3x+2y=6

Substitute y=0 in the given equation.

3x+2(0)=63x+0=63x=63x3=63x=2

The x-intercept is 2. The graph crosses the x-axis at 2,0.

03

– Find the y-intercept.

Substitute x=0 in the given equation.

3(0)+2y=60+2y=62y=62y2=62y=3

The y-intercept is 3. The graph crosses the y-axis at 0,3.

04

– Draw the graph.

Plot the points 2,0and0,3 on a coordinate plane and connect them by a straight line as shown below:

Thus, the x-intercept is 2 and y-intercept is 3.

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