Question

If (a,2) is the point of intersection of the straight lines y = 2x - 4 and y = x + c, then the value of c is equal to
A)-1 C) -2. E) 1 B) 3 D) -3​

Answer 1

y = 2x-4  ---------- (1)

y = a+c --------------(2)

Equationg 1 and 2

2x - 4 = a + c

x - 4  = c  ----------------(3)

As the line intercept at (a,2). Using it on (1)

y = 2x -4

2 = 2(a) - 4

2a = 6

a = 3

a is actually = to x interecpt

so x = 3

using x = 3 in (3)

3 - 4  = C

C = -1

Answer 2

The value of a is equal to -1 (Option A).

Straight lines are said to be defined as two dimensional geometrical entities that are formed by joining various points on the line and is one that can be extended infinitely on both sides.

Linear graphs are ones where the x and y variables are dependent on each other and the plot for linear graphs are always a straight line plots without any curves or bends.

The straight line equation is one such equation that establishes the relationship between two point coordinates lying on the graph which when joined forms the straight line

The equation for straight lines is given by the form:

$y=mx+c$

This is called as the straight line equation which is in slope intercept form.

It is called so because when the slope of a line needs to be found if we consider the slope value as m with coordinates $( x_{1} ,y_{1} )$ and $(x_2} ,y_{2} )$ where x and y are any arbitrary point on the straight line

Here, c is the y intercept which means that the point (0,c) at which the given line intersects the y-axis.

This point would be having the x value as 0 as any point on the y axis will always be as it will parallel to the x axis line.

The given equations are also of the same form as slope intercept form given as:

$y = 2x - 4$

$y = x + c$

The two corresponding straight lines are said to be intersected at a point given as (a,2). The value of c is to be found.

The point (a,2) is the point of intersection and hence would also lie on the line with the equation:

$y = 2x - 4$

Thus, the arbitrary x and y values would be a and 2 respectively and hence, by substituting the values into the equation we have:

$2=2(a)-4$

$\implies 2a=6$

$\implies a=3$

Thus, the unknown value a is found out. The point of intersection will hence be (3,2).

The point of intersection is said to be the point where the two lines cross each other so the point lies on the line with the equation $y = x + c$ as well.

Here, x=3 and y=2. Thus, by substituting the same values we get:

$2=3+c$

$\implies c=2-3$

$\implies c=-1$

Therefore, this is the value of c so the correct option is option A.

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