Select the Graph of the Function that Passes Through (1/2, 5)

Video Solution

Solution Steps

00:05 Let's find out which line the point is on.

00:09 Remember, the left number is X, and the right is Y.

00:13 We'll substitute the point into each line equation to check.

00:19 This one doesn't work, so the point isn't on this line.

00:23 Let's try the next line equation using the same method.

00:26 Substitute the point and see if it fits.

00:30 No luck here; the point isn't on this line either.

00:34 Let's check another line using the same substitution.

00:42 Still no match; the point isn't here.

00:46 Try one more line and substitute the point.

00:51 It fits! The point is on this line.

00:55 And that's how we find the right line for the point!

Step-by-Step Solution

To solve this problem, we'll proceed by comparing each answer choice through substitution:

Choice 1: $y = -4x$
Substitute $x = \frac{1}{2}$ : $y=-4\times\frac{1}{2}=-2$
Does this equal 5? No, so this choice is incorrect.
Choice 2: $y = 4x$
Substitute $x = \frac{1}{2}$ : $y=4\times\frac{1}{2}=2$
Does this equal 5? No, so this choice is also incorrect.
Choice 3: $y = -4x + 3$
Substitute $x = \frac{1}{2}$ : $y=-4\times\frac{1}{2}+3=-2+3=1$
Does this equal 5? No, this choice is incorrect as well.
Choice 4: $4x = y - 3$
Substitute $x = \frac{1}{2}$ and $y = 5$ : $4 \times \frac{1}{2} = 5 - 3 \$ which simplifies to $2 = 2 \$
This equation holds true with the given point.

Therefore, the solution to the problem is $4x = y - 3$ .