Respuesta :
Given the line parallel to the required equation of a line ase are asked tof
[tex]6x-3y=5[/tex]and the point the required line passes through as
[tex](-2,3)[/tex]We can find the equation of the line parallel to 6x-3y=5 and passes through the point (-2,3) below:
Explanation
First, we get the slope of the given line
The general equation of a line(slope -intercept form) is given as
[tex]\begin{gathered} y=mx+c \\ We\text{ would rearrange 6x-3y=5 in the above format} \\ 3y=6x-5 \\ y=\frac{6x-5}{3} \\ y=2x-\frac{5}{3} \\ \therefore By\text{ comparison, slope(m)=2} \end{gathered}[/tex]Since the line given in the questions is parallel to the required line, therefore,
[tex]m_1=m_2[/tex]This implies their slopes are the same.
Next, we can apply all the derived parameters into the point-slope formula for the equation of a line and simplify to get the slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=2(x-(-2)) \\ y-3=2(x+2) \\ y-3=2x+4 \\ y=2x+4+3 \\ y=2x+7 \end{gathered}[/tex]
Therefore the required equation of the line is
Answer: y = 2x + 7
