Answer:
1)[tex]y=3x-1[/tex]
2)[tex]y=\frac{-1}{5}x+4[/tex]
3)[tex]y=5x-3[/tex]
4)[tex]y=3[/tex]
5)[tex]y=\frac{3}{4}x+6[/tex]
6)[tex]y=2x-10[/tex]
7)[tex]y=\frac{3}{2}x+4[/tex]
8)[tex]y=2[/tex]
9)[tex]y=\frac{1}{3}x+3[/tex]
10)y=[tex]y=\frac{-1}{ 2}+4[/tex]
*NOTICE* Some of the numbers on your picture are blurry, so the numbers might be slightly wrong *NOTICE*
Step-by-step explanation:
I assume that this is asking you to write the simplest equation.
The three formulas you need are the slope formula, the point-slope formula and the linear equation.
Slope formula is [tex]\frac{y2-y1}{x2-x1}[/tex] , Point slope is y-y1=m(x-x1), where m is the slope and y1 and x1 come from a point, and linear equation is y=mx+b. Where m is the slope, and b is the y-intercept.
1)Slope=3, and y-intercept=-1, so y=3x-1
2)Slope=-1/5, and y-intercept=4, so y=-1/5x+4
3)Slope=5, and it goes through the point (2,7), so y-7=5(x-2) you distribute the 5 to get y-7=5x-10, and you add the 7 to get y by itself to get y=5x-3
4)Slope=0, and it goes thorough point (-3,3), so y-3=0(x+3). Distribute the zero to get y-3=0. Add thee to get y by itself to get y=3
5)slope=3/4, and it goes through point (0,6), so (0,6) shows that the y-intercept=6. y=3/4x+6
6)Goes through points (6,2) and (5,4), so you use the slope formula to get [tex]\frac{4-2}{6-5}=\frac{2}{1}=2[/tex]. y-2=2(x-6), and you distribute the 2 to get y-2=2x-12. Add two to get y by itself, and you get y=2x-10.
7) Goes through (0,4) and (2,7). Slope formula [tex]\frac{7-4}{2-0}=\frac{3}{2}[/tex]. (0,4) shows the y-intercept=4. y=3/2x+4.
8)Goes through points (-3,2) and (8,2). Slope formula [tex]\frac{2-2}{8-(-3)}=\frac{0}{8+3}=0[/tex]. Point-slope to get y-2=0(x-3). Distribute 0 to get y-2=0. Add 2 to get y by itself to get .
9)Goes through points (-6,1) and (-3,2). Slope formula [tex]\frac{2-1}{-3-(-6)} =\frac{1}{-3+6} =\frac{1}{3}[/tex] . Point-slope to get y-1=1/3(x+6). Distribute 1/3 to get y-1=1/3x+2. Add 1 to get y by itself to get [tex]y=\frac{1}{3}x+3[/tex].
10)y-intercept=4 and goes through point (2,3). Turn y-intercept into point (0,4). Slope formula. [tex]\frac{3-4}{2-0}=\frac{-1}{2}[/tex] . With y-intercept=4, [tex]y=\frac{-1}{2}x+4[/tex]
