Answer:
Step-by-step explanation:
1) slope = 3 ; y-intercept = 1
y = mx + b
y = 3x + 1
0 = 3x + 1 -y
-1 = 3x - y
ANS: 3x - y = -1
2) Passing through (0,2), slope = -4
y - y₁ = m(x -x₁)
y - 2 = -4(x - 0)
y - 2 = -4x
4x + y - 2 = 0
Ans: 4x + y = 2
3)Passing through (-1,3) and (1,1)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{1-3}{1-[-1]}\\\\= \frac{-2}{1+1}\\\\= \frac{-2}{2}\\\\= - 1[/tex]
m= -1 ; (-1 , 3)
y - y₁ = m(x -x₁)
y - 3 = (-1)(x - [-1] )
y -3 = (-1)(x +1 )
y - 3 = -x - 1
x + y -3 = -1
x +y = -1 + 3
Ans: x + y = 2
4) Passing through (1,3), slope = 1/2
y - y₁ = m(x -x₁)
[tex]y - 3 = \frac{1}{2}(x - 1)\\\\y - 3 = \frac{1}{2}x - \frac{1}{2}\\\\[/tex]
Multiply the equation by 2
[tex]2*y - 2*3 = 2*\frac{1}{2}x - 2*\frac{1}{2}\\\\2y - 6 = x - 1\\[/tex]
2y - 6 +1 = x
2y - 5 = x
-5 = x - 2y
Ans: x - 2y = -5
5) Passing through (1/2,1) and (4,2)
Slope = [tex]\frac{2-1}{4-\frac{1}{2}}[/tex]
[tex]= \frac{1}{\frac{7}{2}}\\\\= \frac{2}{7}[/tex]
m = 2/7 ; (4 , 2)
y - y₁ = m(x -x₁)
[tex]y - 2 = \frac{2}{7}(x - 4)\\\\7y - 7*2 = 7*\frac{2}{7}(x - 4)\\\\7y - 14 = 2(x -4)\\\\7y - 14 = 2x - 8\\\\[/tex]
7y - 14 + 8 = 2x
7y - 6 = 2x
Ans: 2x - 7y = -6
