Question

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Answer 1

1. The slope of the line is
`-(1)/(3)`

2. The y-intercept is 4

3. The x-intercept is 12

Explanation:

The Standard Form of a Line

A line can be expressed in several forms, one of which is the called standard form:

Ax + By = C

Other forms may prove useful to know some characteristics of the line, like the slope and intersects.

The given line has the equation:

`1.5x+4.5y=18`

Another form of the line is the slope-intercept:

`y=mx+b`

Where m is the slope and b is the y-intercept of the line.

To convert from the standard form to the slope-intercept form, we solve it for y. It's convenient to eliminate the decimals by multiplying by 2:

`3x+9y=36`

And dividing by 3:

`x+3y=12`

Now subtract x:

`3y=-x+12`

Divide by 3:

`\displaystyle y=(-x+12)/(3)`

Separating fractions:

`\displaystyle y=(-x)/(3)+(12)/(3)`

Operating:

`\displaystyle y=-(1)/(3)x+4`

1. Compare with the slope-intercept form and get:

`\displaystyle m=-(1)/(3)`

The slope of the line is
`-(1)/(3)`

2. The y-intercept can be also obtained from the slope-intercept form: b=4

Thus, the y-intercept is 4

3. The x-intercept can be found by setting y=0 and solving for x in the standard form:

x+3y=12

x+3(0)=12

x=12

The x-intercept is 12