Respuesta :
Given
Point (x,y) = (7,-3)
y-intercept b = 2
Substitute the following values to the slope-intercept form
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex][tex]\begin{gathered} (x,y)=(7,-3) \\ b=2 \\ \\ y=mx+b \\ -3=m(7)+2 \\ -3-2=7m \\ 7m=-5 \\ m=-\frac{5}{7} \end{gathered}[/tex]Now that we have solved for the slope, the equation of the line in slope intercept form is
[tex]\begin{gathered} y=-\frac{5}{7}x+2 \\ \\ \text{Multiply all the terms with 7 to get rid of the fractions} \\ 7\mleft[y=-\frac{5}{7}x+2\mright]7 \\ 7y=-5x+14 \end{gathered}[/tex]Rearrange the equation so that it is in the standard form Ax + By = C
[tex]\begin{gathered} 7y=-5x+14 \\ 5x+7y=-5x+5x+14 \\ 5x+7y=\cancel{-5x+5x}+14 \\ \\ \text{The standard form of the line that passes through }(7,-3)\text{ and has a y-intercept of 2} \\ 5x+7y=14 \end{gathered}[/tex]