Question

John and Nick marked the location of their respective offices on a map. John marked the point (-15,86) and Nick marked the point (25,206)

Write an equation in the slope-intercept form that models the line between the offices of John and Nick.

Answer 1

The equation that models the line between the offices of John and Nick is y = 3x + 131.

Step-by-step explanation:

The equation that models the line between the offices of John and Nick can be found using the slope-intercept form, which is y = mx + b.

First, we need to find the slope (m) of the line. The slope can be calculated using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of John's office are (-15, 86) and the coordinates of Nick's office are (25, 206). Plugging these values into the formula, we get:

m = (206 - 86) / (25 - (-15))

m = 120 / 40

m = 3

Next, we can use one of the points on the line (either John's or Nick's office) to find the y-intercept (b). Let's use John's office (-15, 86). Plugging the values into the slope-intercept form equation, we get:

86 = 3(-15) + b

86 = -45 + b

b = 86 + 45

b = 131

Therefore, the equation that models the line between the offices of John and Nick is y = 3x + 131.