Question

directions: graph each equation by converting to slope - intercept form. show all work!

1. $6x - 2y=-14$

$-2y=-6x - 14$
$y = 3x+7$

1. $x - y=-3$

$-y=-x - 3$
$y=x + 3$

1. $x - 4y=-24$

$-4y=-x - 24$
$y=\frac{1}{4}x + 6$

1. $10x + 4y = 0$

$4y=-10x$
$y=-\frac{5}{2}x$
directions: graph each equation by finding its $x$- and $y$-intercept. show all work!

1. $x - y = 5$

$x$-int
$x-(0)=5rightarrow x = 5$
$y$-int
$0 - y = 5rightarrow y=-5$

1. $x + 5y=-5$

$x$-int
$x+0=-5rightarrow x=-5$
$y$-int
$0 + 5y=-5rightarrow y=-1$

1. $9x + 12y=-36$

$x$-int
$9x+0=-36rightarrow x=-4$
$y$-int
$0 + 12y=-36rightarrow y=-3$

1. $16x - 10y = 20$

$x$-int
$16x-0 = 20rightarrow x=\frac{20}{16}=\frac{5}{4}$
$y$-int
$0 - 10y = 20rightarrow y=-2$

Explanation:

12. Convert to slope-intercept form

Solve for \(y\): \(6x - 2y = -14 \Rightarrow -2y = -6x -14 \Rightarrow y = 3x +7\)
Slope \(=3\), y-intercept \(=7\)

13. Convert to slope-intercept form

Solve for \(y\): \(x - y = -3 \Rightarrow -y = -x -3 \Rightarrow y = x +3\)
Slope \(=1\), y-intercept \(=3\)

14. Convert to slope-intercept form

Solve for \(y\): \(x -4y = -24 \Rightarrow -4y = -x -24 \Rightarrow y = \frac{1}{4}x +6\)
Slope \(=\frac{1}{4}\), y-intercept \(=6\)

15. Convert to slope-intercept form

Solve for \(y\): \(10x +4y =0 \Rightarrow 4y = -10x \Rightarrow y = -\frac{5}{2}x\)
Slope \(=-\frac{5}{2}\), y-intercept \(=0\)

16. Find intercepts

x-intercept (\(y=0\)): \(x -0=5 \Rightarrow x=5\)
y-intercept (\(x=0\)): \(0 - y=5 \Rightarrow y=-5\)

17. Find intercepts

x-intercept (\(y=0\)): \(x +0=-5 \Rightarrow x=-5\)
y-intercept (\(x=0\)): \(0 +5y=-5 \Rightarrow y=-1\)

18. Find intercepts

x-intercept (\(y=0\)): \(9x +0=-36 \Rightarrow x=-4\)
y-intercept (\(x=0\)): \(0 +12y=-36 \Rightarrow y=-3\)

19. Find intercepts

x-intercept (\(y=0\)): \(16x -0=20 \Rightarrow x=\frac{5}{4}\)
y-intercept (\(x=0\)): \(0 -10y=20 \Rightarrow y=-2\)

Answer:

1. \(y=3x+7\)
2. \(y=x+3\)
3. \(y=\frac{1}{4}x+6\)
4. \(y=-\frac{5}{2}x\)
5. x-int=(5,0), y-int=(0,-5)
6. x-int=(-5,0), y-int=(0,-1)
7. x-int=(-4,0), y-int=(0,-3)
8. x-int=(\(\frac{5}{4}\),0), y-int=(0,-2)

(Note: For graphing, plot the intercepts/slope-intercept points and draw the line through them on the provided grids.)