Respuesta :
Answer:
y = 3x - 13................slope= 3, point= (5,2)
y = 3x + 11.................slope= 3, point= (2,17)
3y = x + 11................slope= 1/3, point= (-5,2)
3y = x - 13................slope= 1/3, point= (19,2)
Step-by-step explanation:
To match each equation to its slope and point, remember that an equation in y = mx + b has slope m. The point must also satisfy or make true the equation when substituted for (x,y).
y=3x-13 has slope 3. The point (2,17) make it false. But (5,2) makes it true.
17 = 3(2) - 13 2 = 3(5) - 13
17 = 6-13 2 = 15 - 13
17 = - 7 False 2 = 2 True
y=3x+11 has slope 3. This means (2,17) must be true.
3y=x+11 can be converted to y = 1/3x + 11/3. It has slope 1/3. Test each point.
2= 1/3(19) + 11/3 -2 = 1/3(17) + 11/3 2 = 1/3(-5) + 11/3
2 = 19/3 + 11/3 -2 = 17/3 + 11/3 2 = -5/3 + 11/3
False False 2 = 6/3 True
3y=x-13 can be converted to y = 1/3x - 13/3. It has slope 1/3. Test each remaining point.
2= 1/3(19) - 13/3 -2 = 1/3(17) - 13/3
2 = 19/3 - 13/3 -2 = 17/3 - 13/3
2 = 6/3 -2 = 4/3
True False
Answer:
y=3x-13 : slope = 3, point = (5, 2)
y=3x+11 : slope = 1/3, point = (-5, 2)
3y=x+11 : slope = 3, point = (2,17)
3y=x-13 : slope = 1/3, point = (19, 2)
Step-by-step explanation:
Since, the equation of a line passes through [tex](x_1, y_1)[/tex] with slope m is,
[tex]y-y_1=m(x-x_1)[/tex]
If m = 3, [tex]x_1=2[/tex], [tex]y_1=17[/tex]
Equation of the line,
[tex]y-17=3(x-2)[/tex]
[tex]y-17=3x-6[/tex]
[tex]y = 3x - 6 + 17\implies y = 3x + 11[/tex]
If m = 1/3, [tex]x_1=19[/tex], [tex]y_1=2[/tex]
Equation of the line,
[tex]y-2=\frac{1}{3}(x-19)[/tex]
[tex]3y-6=x-19[/tex]
[tex]3y = x-19+6\implies 3y = x -13[/tex]
If m = 3, [tex]x_1=5[/tex], [tex]y_1=2[/tex]
Equation of the line,
[tex]y-2=3(x-5)[/tex]
[tex]y-2=3x-15[/tex]
[tex]y = 3x - 15 + 2\implies y = 3x -13[/tex]
If m = 1/3, [tex]x_1=17[/tex], [tex]y_1=-2[/tex]
Equation of the line,
[tex]y+2=\frac{1}{3}(x-17)[/tex]
[tex]3y+6=x-17[/tex]
[tex]3y=x-17-6\implies 3y = x-23[/tex]
If m = 1/3, [tex]x_1=-5[/tex], [tex]y_1=2[/tex]
Equation of the line,
[tex]y-2=\frac{1}{3}(x+5)[/tex]
[tex]3y-6=x+5[/tex]
[tex]3y=x+5+6\implies 3y = x+11[/tex]
