The equation of a line in Slope-Interecept form is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
Given the following equation:
[tex]5x+2y=10[/tex]You need to solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 2y=-5x+10 \\ y=\frac{-5x}{2}+\frac{10}{2} \\ \\ y=-2.5x+5 \end{gathered}[/tex]You can see that its slope is:
[tex]m_1=-2.5[/tex]Since the slopes of parallel lines are equal, you know that the slope of the other line is:
[tex]m_2=-2.5[/tex]Substitute the coordinates of the given point and the slope into this equation:
[tex]y=mx+b[/tex]And solve for "b". This is:
[tex]\begin{gathered} 7=-2.5(-6)+b \\ 7=15+b \\ 7-15=b \\ b=-8 \end{gathered}[/tex]Finally, knowing the slope and the y-intercept, you can determine that the equation of this line in Slope-Intercept form, is:
[tex]y=-2.5x-8[/tex]