Find the Linear Function Equation: Slope 6 Through Point (1,-4)

To solve the problem, we will determine the equation of a line using the point-slope form. The general formula for a line in point-slope form is:

$y - y_1 = m(x - x_1)$

Given the slope $m = 6$ and the point $(1, -4)$, we can substitute these values into the formula:

$y - (-4) = 6(x - 1)$

Simplifying the equation, we get:

$y + 4 = 6x - 6$

Now, we want to express this in slope-intercept form $y = mx + b$. So, we solve for $y$:

$y = 6x - 6 - 4$

Finally, combining like terms gives us the equation:

$y = 6x - 10$

Therefore, the equation that represents the function is $y = 6x - 10$.

The correct answer choice is:

: $y=6x-10$