Graph the equation using x and y-intercepts.

For each of these, find two points.

First, enter 0 for x, and solve for y

Then, enter 0 for y, and solve for x.

For instance:  8x + 4y  =  32

First:  let x = 0  --->   8(0) + 4y  =  32

                                  0 + 4y  =  32

                                        4y  =  32

                                          y  =  8     --->  Plot the point (0, 8)

Then:  let y = 0   --->   8x + 4(0)  =  32

                                    8x + 0  =  32

                                          8x  =  32

                                            x  =  4     --->  Plot the point (4, 0)

Then draw the line that passes through the points  (0, 8)  and  (4, 0).

Graph the equation using x and y-intercepts.

9. 8x + 4y = 32

10. –6x + 5y = –30

11. –4x – 5y = 20

12. 6x + 8y = 48

13. 3x + 7y = 21

14. 6x – 7y = –42

15. –3x + 3y = –9

16. 7x – 2y = –14

For all equations it is the same:  a*x+b*y = a*b
so

$\begin{array}{lrcl} & a\cdot x + b \cdot y &=& a \cdot b \qquad | \qquad : (a\cdot b) \\ & \frac{ a\cdot x }{ a\cdot b } + \frac{ b \cdot y }{ a\cdot b } &=& 1 \\ & \frac{ x }{ b } + \frac{ y }{ a } &=& 1 \\ \\ \hline \\ \text{ y-intercept} (x = 0): &\frac{ y }{ a } &=& 1\\ &\mathbf{ y }& \mathbf{=} & \mathbf{a}\\ \\ \hline \\ \text{ x-intercept} (y = 0): &\frac{ x }{ b } &=& 1\\ &\mathbf{ x }& \mathbf{=} & \mathbf{b}\\ \end{array}$

So connect (0,a) with (b,0) to draw the line

We have:

$\begin{array}{rrcr|r|r|c} \hline & & & & a= & b= & \text{connect} \\ \hline 9. & 8x + 4y &=& 32 & 8&4 & (0,8) ~ \rightarrow ~ (4,0) \\ 10.& –6x + 5y &=& –30 & -6&5 & (0,-6) ~ \rightarrow ~ (5,0) \\ 11.& –4x – 5y &=& 20 & -4&-5 & (0,-4) ~ \rightarrow ~ (-5,0) \\ 12.& 6x + 8y &=& 48 & 6&8 & (0,6) ~ \rightarrow ~ (8,0) \\ 13.& 3x + 7y &=& 21 & 3&7 & (0,3) ~ \rightarrow ~ (7,0) \\ 14.& 6x – 7y &=& –42 & 6&-7 & (0,6) ~ \rightarrow ~ (-7,0) \\ 15.& –3x + 3y &=& –9 & -3&3 & (0,-3) ~ \rightarrow ~ (3,0) \\ 16.& 7x – 2y &=& –14 & 7&-2 & (0,7) ~ \rightarrow ~ (-2,0) \\ \hline \end{array}$