Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Indicate in standard form the equation of the line passing through the given points.
P(6, 2), Q(8, -4)

Answer 1

To find the standard form equation of a line passing through two points, calculate the slope using the coordinates, use the point-slope form, and then convert it to standard form.

Step-by-step explanation:

The correct answer is option standard form equation of the line. To find the equation of the line that passes through points P(6, 2) and Q(8, -4), we first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of the points P and Q, respectively. After finding the slope, we use the point-slope form of the line equation: y - y1 = m(x - x1) and substitute either point into this equation to solve for y. This will give us the slope-intercept form of the equation, which can then be converted to standard form (Ax + By = C), where A, B, and C are integers, and A should be non-negative.

In this particular case, the slope m becomes ((-4) - 2) / (8 - 6), which simplifies to -6 / 2 = -3. The slope-intercept form using point P(6, 2) would be y - 2 = -3(x - 6). Simplifying, y = -3x + 20. Converting to standard form gives us 3x + y = 20, which is the final answer.