Question

Suppose that a line passes through the points (4,-3) and (1,6). Where will it pass through the x-axis?

Option 1: (7,0)
Option 2: (-7,0)
Option 3: (2,0)
Option 4: (-2,0)

Answer 1

The line passing through the points (4,-3) and (1,6) intersects the x-axis at (3,0), which is not listed in the given options.

Step-by-step explanation:

To find where a line passes through the x-axis, we need to find the point where y is 0. Given two points that a line passes through, such as (4,-3) and (1,6), we first calculate the slope of the line.

The slope (m) can be calculated by the formula:

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

For our points, it will be:

m = (6 - (-3)) / (1 - 4)

m = 9 / -3

m = -3

Now we use one of the points and the slope to find the equation of the line in the slope-intercept form (y=mx+b).

Substituting point (4, -3) into the slope-intercept formula:

-3 = (-3)*4 + b

b = -3 + 12

b = 9

So, the equation of the line is:

y = -3x + 9

To find where the line intersects the x-axis, set y to 0 and solve for x:

0 = -3x + 9

3x = 9

x = 3

Therefore, the line passes through the x-axis at (3,0), which is not provided in the options.