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