Respuesta :
For this type of question the first step is to calculate the slope of the line given by th equation x+2y=7, for this we recall the slope intercept form ( y=mx+b) and put the equation in that form
[tex]y=-\frac{x}{2}+\frac{7}{2}[/tex]Then, m=-1/2. Now, since the equation of the line we are looking for is parallel to the previous line the slope must be the same, now we recall the point slope equation
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ \end{gathered}[/tex]Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :
[tex]\begin{gathered} y-4=-\frac{1}{2}(x-(-3)) \\ y-4=-\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]Finally to put it in the slope intercept form, we solve the equation for y:
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]For part b) we recall that the standard form of the equation of a line is:
[tex]\begin{gathered} C=Ax+By \\ \text{where C, A and B are real and whole numbers if possible} \end{gathered}[/tex]Now, we solve for the constant of the equation:
[tex]\begin{gathered} \frac{5}{2}=y+\frac{1}{2}x \\ 5=2y+x \end{gathered}[/tex]The last equation is the standard form of the equation of the line.
