To find the equation of a line in standard form that passes through the points \((4, -6)\) and \((8, 10)\), we first need to calculate the slope, \(m\), using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points \((x_1, y_1) = (4, -6)\) and \((x_2, y_2) = (8, 10)\):
\[ m = \frac{10 - (-6)}{8 - 4} = \frac{10 + 6}{4} = \frac{16}{4} = 4 \]
Now we have the slope \(m = 4\). Next, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point \((4, -6)\):
\[ y - (-6) = 4(x - 4) \]
This simplifies to:
\[ y + 6 = 4x - 16 \] \[ y = 4x - 16 - 6 \] \[ y = 4x - 22 \]
Now, to convert this equation into standard form \(Ax + By = C\), we rearrange it:
\[ -4x + y = -22 \]
Multiplying the entire equation by \(-1\) to make \(A\) positive:
\[ 4x - y = 22 \]
Thus, in standard form, the equation of the line is:
\[ 4x - y = 22 \]
Looking at the provided options, we see that this matches option A:
A \(4x - y = 22\)
So the correct answer is:
A \(4x - y = 22\)
3 answers