Question

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,4) and parallel to x + 2y = 7.a) The equation of the line in slope-intercept form is(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)b) The equation of the line in standard form is(Type your answer in standard form.)

Answer 1

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

`y=-(x)/(2)+(7)/(2)`

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

`\begin{gathered} (y-y_1)=m(x-x_1) \\ \end{gathered}`

Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :

`\begin{gathered} y-4=-(1)/(2)(x-(-3)) \\ y-4=-(1)/(2)x-(3)/(2) \end{gathered}`

Finally to put it in the slope intercept form, we solve the equation for y:

`y=-(1)/(2)x+(5)/(2)`

For part b) we recall that the standard form of the equation of a line is:

`\begin{gathered} C=Ax+By \\ \text{where C, A and B are real and whole numbers if possible} \end{gathered}`

Now, we solve for the constant of the equation:

`\begin{gathered} (5)/(2)=y+(1)/(2)x \\ 5=2y+x \end{gathered}`

The last equation is the standard form of the equation of the line.