Write an equation in point-slope form for the line that passes through the given points. (1, –3), (4, –15)

To write the equation of a line in point-slope form, we first need to determine the slope (m) using the two given points: (1, -3) and (4, -15).

1. Calculate the slope (m) using the formula:

[

m = frac{y_2 – y_1}{x_2 – x_1} = frac{-15 – (-3)}{4 – 1} = frac{-15 + 3}{3} = frac{-12}{3} = -4

]

2. Use the point-slope form equation:

The point-slope form is given by:

[

y – y_1 = m(x – x_1)

]

We can use either of the given points. Let’s use (1, -3):

[

y – (-3) = -4(x – 1)

]

This simplifies to:

[

y + 3 = -4(x – 1)

]

So, the point-slope form of the line is:

[

y + 3 = -4(x – 1)

]

This equation represents the line passing through the points (1, -3) and (4, -15). If you have any further questions or need more detailed explanations, feel free to ask!