Write an equation in point-slope form for the line that passes through the given points. (-4, 6), (-2, 22)

To find the equation of the line in point-slope form that passes through the points ((-4, 6)) and ((-2, 22)), we first need to calculate the slope (m) of the line using the formula:

[

m = frac{y_2 – y_1}{x_2 – x_1}

]

Using the points, let’s denote:

– ((x_1, y_1) = (-4, 6))

– ((x_2, y_2) = (-2, 22))

Now, substitute the values into the formula:

[

m = frac{22 – 6}{-2 – (-4)} = frac{16}{2} = 8

]

Now, we can use the point-slope form of a line, which is given by:

[

y – y_1 = m(x – x_1)

]

Using point ((-4, 6)) and the slope (m = 8):

[

y – 6 = 8(x – (-4))

]

[

y – 6 = 8(x + 4)

]

Thus, the equation in point-slope form is:

[

y – 6 = 8(x + 4)

]

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