Graph Intersection: Points on the Line y=2(x+2)-1

Video Solution

Solution Steps

00:00 Find which points are on the line

00:03 Open parentheses properly, multiply by each factor

00:11 This is the equation of the line

00:15 In each point, the left number represents the X-axis and the right represents Y

00:19 Let's substitute each point in the line equation and see if it's possible

00:27 Not possible, therefore the point is not on the line

00:32 We'll use the same method for all points to find which ones are on the line

00:35 Let's move to this point

00:47 Not possible, therefore the point is not on the line

01:06 Possible, therefore the point is on the line

01:12 Let's move to this point

01:21 Not possible, therefore the point is not on the line

01:25 And this is the solution to the question

Step-by-Step Solution

To determine through which points the function $y = 2(x+2) - 1$ passes, let's proceed methodically.

Step 1: Simplify the expression of the linear function:

The given function is $y = 2(x+2) - 1$ . Distribute the $2$ over the terms inside the parenthesis:
$y = 2x + 4 - 1$

Simplify further by combining like terms:
$y = 2x + 3$

Step 2: Evaluate the function at different $x$ -values to find which points lie on the line represented by the function $y = 2x + 3$ .

Step 3: Check each of the provided choice points:

For choice $(0,0)$ : Substituting $x = 0$ into $y = 2x + 3$ , we get $y = 2(0) + 3 = 3$ . This does not match $y = 0$ .
For choice $(10,13)$ : Substituting $x = 10$ into $y = 2x + 3$ , we get $y = 2(10) + 3 = 23$ . This does not match $y = 13$ .
For choice $(5,13)$ : Substituting $x = 5$ into $y = 2x + 3$ , we get $y = 2(5) + 3 = 13$ . This matches $y = 13$ , so this point lies on the line.
For choice $(4,13)$ : Substituting $x = 4$ into $y = 2x + 3$ , we get $y = 2(4) + 3 = 11$ . This does not match $y = 13$ .

Therefore, the point through which the given function passes is $(5,13)$ .