Question

find the coordinates of the x intercept of the line passing through point (2,5) with slope 3/2 using calculations.

Answer 1

To find the x-intercept, we need to find the point where the line crosses the x-axis, which means the y-coordinate of this point is 0.

Given point (2,5) on the line and slope 3/2, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Substitute the values (2,5) and 3/2 for x1, y1, and m:

y - 5 = (3/2)(x - 2)

Now, we need to set y = 0 to find the x-coordinate of the x-intercept:

0 - 5 = (3/2)(x - 2)
-5 = (3/2)x - 3
-5 + 3 = (3/2)x
-2 = (3/2)x
-4/3 = x

Therefore, the x-intercept is at the point (-4/3, 0).