Given:
Equation of line
[tex]y+4=-\frac{3}{2}(x-7)[/tex]And a point (1,2).
Required:
To find the equation of the line that is parallel to the given line and passes through from the given point.
Explanation:
The given equation is:
[tex]y+4=-\frac{3}{2}(x-7)[/tex]Write the equation in slope-intercept form y= mx+b.
[tex]\begin{gathered} y+4=-\frac{3}{2}x+\frac{21}{2} \\ y=-\frac{3}{2}x+\frac{21}{2}-4 \\ y=-\frac{3}{2}x+\frac{21-4\times2}{2} \\ y=-\frac{3}{2}x+\frac{13}{2} \end{gathered}[/tex]Compare this equation with y=mx+b, we get
[tex]m=-\frac{3}{2}[/tex]The slope of the parallel lines is equal. So the line that is parallel to the given lime has the same slope.
The equation of line has slope m and passes through from the point
[tex](x_1,y_1)[/tex]is given by the formula:
[tex]y-y_1=m(x-x_1)[/tex]Thus the equation of the line passes through from the point (1,2) and has slope m= -3/2 is:
[tex]\begin{gathered} y-2=-\frac{3}{2}(x-1) \\ y-2=-\frac{3}{2}x+\frac{3}{2} \\ y=-\frac{3}{2}x+\frac{3}{2}+2 \\ y=-\frac{3}{2}x+\frac{3+2\times2}{2} \\ y=-\frac{3}{2}x+\frac{7}{2} \end{gathered}[/tex]Final Answer:
The equation of the line that is parallel to the given line and passes through from the point (1,2) is
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]