Goes through the points $$ (5,-2) $$ and $$ (8,13) $$ $$ y=5 x-27 $$

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To determine if the line represented by the equation $$ y = 5x - 27 $$ goes through the points $$ (5, -2) $$ and $$ (8, 13) $$, we will substitute the x-coordinates of each point into the equation and check if the corresponding y-coordinates match.

### Step 1: Check the point $$ (5, -2) $$

Substituting $$ x = 5 $$ into the equation:

$$
y = 5(5) - 27
$$

Calculating this gives:

$$
y = 25 - 27 = -2
$$

Since the calculated $$ y $$ value matches the y-coordinate of the point $$ (5, -2) $$, this point lies on the line.

### Step 2: Check the point $$ (8, 13) $$

Now, substituting $$ x = 8 $$ into the equation:

$$
y = 5(8) - 27
$$

Calculating this gives:

$$
y = 40 - 27 = 13
$$

Since the calculated $$ y $$ value matches the y-coordinate of the point $$ (8, 13) $$, this point also lies on the line.

### Conclusion

Both points $$ (5, -2) $$ and $$ (8, 13) $$ lie on the line represented by the equation $$ y = 5x - 27 $$.
Both points $$ (5, -2) $$ and $$ (8, 13) $$ lie on the line $$ y = 5x - 27 $$.

Goes through the points \( (5,-2) \) and \( (8,13) \) \( y=5 x-27 \)

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