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

A linear function with a slope of 6 passes through the point $(1,1)$.

Which equation represents the function?

To solve the problem of finding the equation of the linear function, we will use the point-slope form, which is:

Step-by-step:

• Step 1: Identify given information: The slope $m = 6$ and the point $(x_1, y_1) = (1, 1)$.

• Step 2: Substitute the slope and point into the point-slope form:

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

• Step 3: Simplify the equation:

  $y - 1 = 6x - 6$

• Step 4: Solve for $y$ to express in slope-intercept form $y = mx + b$:

  $y = 6x - 6 + 1$

• Step 5: Simplify the right-hand side:

  $y = 6x - 5$

Thus, the equation of the linear function is $y = 6x - 5$.