Respuesta :

y - 6 = 3/2 (x + 5)     no
y - 4 = 2/3 (x - 2)     yes
y - 4 = 3/2 (x + 2)     no
y - 6 = 2/3 (x - 5)     yes
y - 6 = 2/3 (x + 5)     no
y - 6 = 3/2 (x - 5)     it only goes through (5, 6), so I'm assuming that would also be no?

Hope this helps!
calculista

Answer:

The answer in the attached figure

Step-by-step explanation:

we know that

The equation of the line in point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]A(2,4)\ B(5,6)[/tex]

Step 1

Find the slope of the line m

The formula to calculate the slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substitute the values

[tex]m=\frac{6-4}{5-2}[/tex]

[tex]m=\frac{2}{3}[/tex]

Step 2

Find the equation of the line with point A and the slope m

we have

[tex]m=\frac{2}{3}[/tex]

[tex]A(2,4)[/tex]

Substitute the values

[tex]y-4=\frac{2}{3}(x-2)[/tex]

Step 3

Find the equation of the line with point B and the slope m

we have

[tex]m=\frac{2}{3}[/tex]

[tex]B(5,6)[/tex]

Substitute the values

[tex]y-6=\frac{2}{3}(x-5)[/tex]


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