The y and x interceps of the equation 2x + 3y = 6

Question

find the intercepts and graph the equation.

 

Answer 1

Given line 2x+3y= 6 ---> (1)

To find x intercept substitute y = 0 in (1).

2x = 6

Divide to eachside by 2.

x = 3

To find y intercept substitute x = 0 in (1).

3y = 6

Divide to eachside by 3.

y = 2

x intercept is 3 and y intercept is 2.

Graph

Answer 2

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

The equation is 2x + 3y = 6.

Write the equation in intercept - form.

2x /6 + 3y /6 = 1

x /(6/2) + y /(6/3) = 1

x /3 + y /2 = 1.

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

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

• Write the equation in slope-intercept form y = mx + b, where m is slope and b is y -intercept.

The equation is 2x + 3y = 6.

3y = - 2x + 6

y = (- 2/3)x + 2.

Compare the equation with slope - intercept form y = mx + b.

slope = - 2/3 and y - intercept is 2.

y - intercept is 2, so the line crosses the y - axis at (0, 2)

Using slope find the next point.

Slope = rise/run = - 2/3

Start at point (0, 2), move 2 units down and 3 units right, then plot the point (3, 0).

Draw a line through these points.

Graph :