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Sagot :
To find the equation of the line (line 1) that passes through the points (2,4) and is parallel to the line 3x - 2y = 18 (line 2), you can follow the steps above.
Step 1) Write the equation of line 2 in the slope-intercept form.
A general equation for the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
So, let's isolate y in line 2:
3x - 2y = 18
3y - 18 =2y
2y = 3x - 18
y = 3/2x - 18/2
y = 3/2x - 9
Step 2) Find the slope of line 1.
Since line 1 and 2 are parallel, they have the same slope.
So,
[tex]m_1=m_2=\frac{3}{2}[/tex]Step 3) Find the y-intercept (b) for line 1.
The equation for line 1 is
[tex]y=\frac{3}{2}x+b[/tex]To find b, we substitute the point (2,4) in the equation:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ 4=\frac{3}{2}\cdot2+b \\ 4=\frac{6}{2}+b \\ 4=3+b \\ 4-3=b \\ b=1 \end{gathered}[/tex]Step 4) Write the equation of the line.
Since you found m and b, you can write the equation of the line:
[tex]y=\frac{3}{2}x+1[/tex]Answer:
[tex]y=\frac{3}{2}x+1[/tex]
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