¿cuántas de las ecuaciones indicadas a continuación representan la
línea que pasa por los puntos (2,3) y (4, -- 7)?
5x + y = 13
y + 7 = –5(x – 4)
y = –5x + 13
y –7 = 5(x – 4)

5x + y = 13 / y = -5x + 13

Step-by-step explanation:

If you want to know if these points are in a equation, you have to check each point in each equation.

So.. let's try. We have the first point (2,3). Now, we're checking in the first equation:

5 . (2) + (3) = 13 (this is a true sentence)

Let's try the another point (4, -7)

5.(4) + (-7) = 13 (this is a true sentence as well)

the second one: y + 7 = -5(x + 4)

3 + 7 = -5(2+6) (it isn't true. So, I won't try the another point).

the third one: y = -5x + 13

(3) = -5.(2) + 13 (this is a true sentence. Let's check now the another point).

(-7) = -5(4) + 13 (this is a true sentence as well).

the fourth one: y - 7 = 5(x + 4)

(3)  - 7 = 5(2 + 4) (it isn't true. I won't check the another point).

Finally, we have as a answer the first and the third equations.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl