Question

- Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection , x/3-y/5=4 and 3x/4+2y/3=6.

Answer 1

Given that :

The equations are and

For x-intercepts substitute the value in the equations

and

The x-intercepts points are .

For y-intercepts substitute the value in the equations

and

The y-intercepts points are .

The graph of the two lines and is,

Graph :

From the graph

The intersection point is .

Answer 2

The intercept - form of a line equation is x/a+ y/b = 1, where a and b are xand y intercepts.

• The first line equation is x/3 - y/5 = 4.

Write the equation in intercept - form.

x/12 - y/20 = 1

x/12 + y/(-20) = 1.

Compare the above equation with intercept - form of a line equation.

x - intercept is 12.

So, the line crosses the x - axis at the point (12, 0).

And y - intercept is - 20.

So, the line crosses the y - axis at the point (0, - 20).

• The second line equation is 3x/4 + 2y/3 = 6.

Write the equation in intercept - form.

3x/24 + 2y/18 = 1

x/8 + y/9 = 1.

Compare the above equation with intercept - form of a line equation.

x - intercept is 8.

So, the line crosses the x - axis at the point (8, 0).

And y - intercept is 9.

So, the line crosses the y - axis at the point (0, 9).

• Graph :

1) Draw the coordinate plane.

2) Plot the points of two lines.

3) Connect the lines through the plotted points.

Observe the graph, The two lines intersects at a point (10.38, - 2.38).