Question

Find the value of a, if the point (3,4) lies on the graph of ax-4y+10=0. Also, find the coordinates of the point on the graph for which y=1.

Answer 1

Given,

Point (3, 4) lies on the line ax - 4y+ 10 = 0.

To find,

Value of a, and,

The coordinates of a point on the graph where y = 1.

Solution,

Here, the given equation of the line is,

ax - 4y + 10 = 0.

Further, it is given that point (3, 4) lies on this line. So, this point (3, 4) must satisfy the equation.

Substituting the coordinates that is, x = 3, y = 4, in the equation.

⇒ a(3) - 4(4) + 10 = 0

⇒ 3a - 16 + 10 = 0

⇒ 3a - 6 = 0

⇒ 3a = 6

⇒ a = 2

Substituting this value in the given equation, it becomes,

2x - 4y + 10 = 0

Now, we have to find x for which y = 1. So putting y = 1 in the above new obtained equation, we get,

2x - 4(1) + 10 = 0

⇒ 2x - 4 + 10 = 0

⇒ 2x + 6 = 0

⇒ 2x = -6

⇒ x = -3

So, the coordinates of the point where y = 1, will be (-3, 1)

Therefore, the value of a for the given equation will be 2, and the point at which y = 1, will be (-3, 1).

Answer 2

Answer:

The value of the missing variable a is found to be 2 and the coordinate of the graph at y=1 is found to be (-3,1).

Step-by-step explanation:

The given linear equation for the graph is:  $ax-4y+10=0$

We are given that the point $(3,4)$ is lying on the graph of the equation $ax-4y+10=0$,

So, substituting the point coordinates in the equation, we get:

$a(3)-4(4)+10=0$

$3a-16+10=0$

Simplifying it, we get:

$3a=6$

or

$a=2$

So, the complete equation for the graph is: $2x-4y+10=0$

Now, to find the coordinates at y=1, we substitute this in the equation to get:

$2x-4(1)+10=0$

$2x-4+10=0$

Simpifying it, we get:

$2x=-6$

or

$x=-3$

So, the coordinate of point on the graph at $y=1$ is $(-3,1)$.