Answer:
1. The slope of the line is [tex]-\frac{1}{3}[/tex]
2. The y-intercept is 4
3. The x-intercept is 12
Step-by-step 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:
[tex]1.5x+4.5y=18[/tex]
Another form of the line is the slope-intercept:
[tex]y=mx+b[/tex]
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:
[tex]3x+9y=36[/tex]
And dividing by 3:
[tex]x+3y=12[/tex]
Now subtract x:
[tex]3y=-x+12[/tex]
Divide by 3:
[tex]\displaystyle y=\frac{-x+12}{3}[/tex]
Separating fractions:
[tex]\displaystyle y=\frac{-x}{3}+\frac{12}{3}[/tex]
Operating:
[tex]\displaystyle y=-\frac{1}{3}x+4[/tex]
1. Compare with the slope-intercept form and get:
[tex]\displaystyle m=-\frac{1}{3}[/tex]
The slope of the line is [tex]-\frac{1}{3}[/tex]
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
