Linear Function Equation: Finding the Line with Slope 1 Through (6,13)

A linear function has a slope of 1 and passes through the point $(6,13)$.

Choose the equation that represents this function.

To solve this problem, we'll follow these steps:

• Step 1: Use the point-slope form with the given point and slope.

• Step 2: Simplify the equation to slope-intercept form.

• Step 3: Identify the correct equation from the options.

Now, let's work through each step:

Step 1: Apply the point-slope form formula:
Given the point $(6, 13)$ and the slope $m = 1$, the point-slope form is:
$y - 13 = 1(x - 6)$

Step 2: Simplify to get the equation in slope-intercept form:
$y - 13 = 1 \cdot (x - 6) \\ y - 13 = x - 6 \\ y = x - 6 + 13 \\ y = x + 7$

Step 3: Compare to find the correct answer:
From the simplified equation $y = x + 7$, the correct choice is:

$y=x+7$

Therefore, the equation representing the function is $y = x + 7$.