Slope Intercept Form of a Line Practice AK

Find the slope and y intercept from each equation of the line

1. $m=-3, b=9$

2. $m=-\dfrac{2}{3}, b=-7$

3. 
$\eqalign{y&=8+\dfrac{x}{-3}\\y&=\dfrac{x}{-3}+8\\m&=\dfrac{-1}{3}, b=8}$

4.

$\eqalign{y&=\dfrac{18+2x}{4}\\y&=\dfrac{9}{2}+\dfrac{1}{2}x\\y&=\dfrac{1}{2}x+\dfrac{9}{2}\\m&=\dfrac{1}{2},b=\dfrac{9}{2}}$

5. $m=0, b=7$

6. $m=$ undefined/no slope, $b=$ does not exist 

Write an equation of a line in slope intercept form

7. $y=3x-5$

8. $y=-\dfrac{3}{8}x+9$

9. $y=\dfrac{-2}{7}x$

10. $y=-2$ 

11. $y=\dfrac{1}{8}x+7$

Rearrange the equations into slope intercept form.

12. 
$\eqalign{&3y+2x=6\\&3y=-2x+6\\&y=-\dfrac{2}{3}x+2}$

13. 
$\eqalign{&-5x+2y=-16\\&2y=5x-16\\&y=\dfrac{5}{2}x-8}$

14. 
$\eqalign{&2x=-7y-5\\&7y=-2x-5\\&y=\dfrac{-2}{7}x-\dfrac{5}{7}}$

Graph the following equations.

15. $y=2x-4$

16. $y=x-3$

17. $y=\dfrac{-6}{7}x+4$

18.

$\eqalign{&2y=3x-8\\&\dfrac{2y}{2}=\dfrac{3x-8}{2}\\&y=\dfrac{3}{2}x-4}$

19.

$\eqalign{&-3x+3y=18\\&3y=3x+18\\&\dfrac{3y}{3}=\dfrac{3x+18}{3}\\&y=x+6}$

20.

$\eqalign{&4x-5y=30\\&-5y=-4x+30\\&\dfrac{-5y}{-5}=\dfrac{-4x+30}{-5}\\&y=\dfrac{4}{5}-6}$

21.

$\eqalign{y=\dfrac{3}{4}x+b\\2=\dfrac{3}{4}(8)+b\\2=6+b\\b=-4\\y=\dfrac{3}{4}x-4}$

22.

$\eqalign{\dfrac{3-2}{3-8}=\dfrac{-1}{-5}=\dfrac{1}{5}\\m=\dfrac{1}{5}\\y=\dfrac{1}{5}x+b\\3=\dfrac{1}{5}(3)+b\\3=\dfrac{3}{5}+b\\\dfrac{12}{5}=b\\y=\dfrac{1}{5}x+\dfrac{12}{5}}$

23. Passes through (0,0).  b=0. $y=\dfrac{-2}{3}x$

24. Slope = 2. $\eqalign{y=2x+b\\4=2(1)+b\\b=2\\y=2x+b}$

25.

$\eqalign{\dfrac{3-5}{4-10}=\dfrac{-2}{-6}=\dfrac{1}{3}\\m=\dfrac{1}{3}\\y=\dfrac{1}{3}x+b\\3=\dfrac{1}{3}(4)+b\\3=\dfrac{4}{3}+b\\\dfrac{5}{3}=b\\y=\dfrac{1}{3}x+\dfrac{5}{3}}$