Answer :
For Parallelism condition, the slope of the two(2) lines are equal.
i.e:
[tex]m_1=m_2[/tex]From the given equation of the line:
[tex]y=-5x+3[/tex]Comparing this with the standard straight line equation: y= mx + c, where m represents the slope, we have:
[tex]m=-5[/tex]Since the lines are parallel; the new slope is also equal to -5.
Thus,
[tex]\begin{gathered} m_1=m_2 \\ m_2=-5 \end{gathered}[/tex]Now that we know the slope and a point (5, -2), we can use the slope formula:
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ m=-5 \\ \text{from the point (5,2);} \\ x_1=5,y_1=2 \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} -5=\frac{y-2}{x-5} \\ \text{cross}-\text{multiply;} \\ y-2=-5(x-5) \\ y-2=-5x+25 \\ y=-5x+25+2 \\ y=-5x+27 \end{gathered}[/tex]Hence, the equation in slope-intercept form is:
[tex]y=-5x+27[/tex]