Question

What is the equation of the line passing through the points (2,8) and (7,2) in point-slope form?

Answer 1

You can use either y - 8 = -6/5(x - 2) or y - 2 = -6/5(x - 7)

Step-by-step explanation:

The general equation of the point-slope form is given by:

y - y1 = m(x - x1), where:

• (x1, y1) is any point on the line,
• and m is the slope.

Finding the slope:

We can find the slope using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where:

• m is the slope,
• (x1, y1) is one point on the line,
• and (x2, y2) is another point on the line.

Thus, we can find the slope by substituting (2, 8) for (x1, y1) and (7, 2) for (x2, y2) in the slope formula:

m = (2 - 8) / (7 - 2)

m = -6/5

Thus, the slope of the line is -6/5

Writing the equation in point-slope form:

Now, we can write the equation of the line in point-slope form by substituting -6/5 for m and (2, 8) for (x1, y1) in the general equation of the point-slope form:

y - 8 = -6/5(x - 2)

Therefore, y - 8 = -6/5(x - 2) is the equation of the line in point-slope form that passes through the points (2, 8) and (7, 2).

Writing the equation using (7, 2) for (x1, y1):

If you were to use (7, 2) for (x1, y1) instead, the equation would be:

y - 2 = -6/5(x - 7)

Answer 2

The equation of the line passing through the points (2,8) and (7,2) in point-slope form is y - 8 = (-6/5)(x - 2).

Step-by-step explanation:

To find the equation of a line in point-slope form, we need to first find the slope and then use one of the given points along with the slope in the equation. The slope is defined as the change in y divided by the change in x between two points. Let's calculate the slope using the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Given the points (2,8) and (7,2), we can substitute the values into the formula:

Slope (m) = (2 - 8) / (7 - 2) = -6 / 5

Now we have the slope, we can choose one of the points, for example (2,8), and use the point-slope form equation: y - y1 = m(x - x1).

Substituting the values, we get: y - 8 = (-6/5)(x - 2)

This is the equation of the line passing through the points (2,8) and (7,2) in point-slope form.