Find the Linear Function Equation: Slope 5 Through Point (2,4)

To solve for the equation of a line given a slope and a point:

• Step 1: Use the point-slope form of the linear equation: $y - y_1 = m(x - x_1)$.
• Step 2: Substitute the given slope $m = 5$ and point $(2, 4)$ into the equation.
• Step 3: Simplify and rearrange to convert into slope-intercept form $y = mx + b$.

Substituting into the point-slope form, we have:

$y - 4 = 5(x - 2)$

Distribute the 5 across the terms in the parentheses:

$y - 4 = 5x - 10$

Add 4 to both sides to solve for $y$:

$y = 5x - 10 + 4$

This simplifies to:

$y = 5x - 6$

Therefore, the equation of the line is $y = 5x - 6$.

The correct choice among the options given is $y = 5x - 6$.