+472 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
+23252 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).
+26393 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:
\(\begin{array}{rrcr|r|r|c} \hline & & & & a= & b= & \text{connect} \\ \hline 9. & 8x + 4y &=& 32 & 8&4 & (0,8) ~ \rightarrow ~ (4,0) \\ 10.& –6x + 5y &=& –30 & -6&5 & (0,-6) ~ \rightarrow ~ (5,0) \\ 11.& –4x – 5y &=& 20 & -4&-5 & (0,-4) ~ \rightarrow ~ (-5,0) \\ 12.& 6x + 8y &=& 48 & 6&8 & (0,6) ~ \rightarrow ~ (8,0) \\ 13.& 3x + 7y &=& 21 & 3&7 & (0,3) ~ \rightarrow ~ (7,0) \\ 14.& 6x – 7y &=& –42 & 6&-7 & (0,6) ~ \rightarrow ~ (-7,0) \\ 15.& –3x + 3y &=& –9 & -3&3 & (0,-3) ~ \rightarrow ~ (3,0) \\ 16.& 7x – 2y &=& –14 & 7&-2 & (0,7) ~ \rightarrow ~ (-2,0) \\ \hline \end{array}\)
