Respuesta :
Answer:
The slope is 0.3.
Step-by-step explanation:
1.5x + 4.5y = 18
4.5y = 18 - 1.5x
4.5 4.5
y = 4 - 0.3x
The slope of a straight line equation is given by the slope and intercept form of the equation
The slope of the graph of 1.5·x + 4.5·y = 18 is -0.[tex]\overline 3[/tex]
The reason why the slope is correct is given as follows:
The given equation is 1.5·x + 4.5·y = 18
Required:
To find the slope of the graph formed by the function
Solution:
The highest and only power of the two variables in the function is one, therefore;
The function is a linear function
The slope and intercept form of a straight line equation is y = m·x + c
Where;
m = The slope of the graph of the function
c = The y-intercept of the function
Therefore, to find the slope, the given function can be rearranged into the form y = m·x + c, as follows;
1.5·x + 4.5·y = 18
4.5·y = 18 - 15·x
[tex]\displaystyle \dfrac{4.5 \cdot y}{4.5} = \frac{18}{4.5} - \frac{1.5 \cdot x}{4.5}[/tex]
[tex]\displaystyle y= 4- \frac{1 }{3} \cdot x = 4 - 0.\overline 3 \cdot x = - 0.\overline 3 \cdot x + 4[/tex]
By comparing y = -0.[tex]\bar 3[/tex]·x + 4 to y = m·x + c, we have;
The slope of the graph, m = -0.[tex]\bar 3[/tex]
Therefore, the slope of the graph, 1.5·x + 4.5·y = 18 which is the same equation as y = -0.[tex]\bar 3[/tex]·x + 4, is m = -0.[tex]\bar 3[/tex]
Alternatively, from the equation and graph, we have;
When x = 0
1.5×0 + 4.5·y = 18
y = 4
When y = 0
1.5×x + 4.5×0 = 18
x = 12
[tex]Slope = \dfrac{4 - 0}{0 - 12} = -\dfrac{1}{3} = -0.\overline 3[/tex]
Learn more about the slope and intercept form of a linear equation here;
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