Question

It can be shown that the line with intercepts (a, 0) and (0, b) has the following equation:

x/a + y/b= 1, a ≠ 0, b ≠ 0.

Use this result to write an equation of the line.

Point on line:

(−2, 4)

x-intercept: (a, 0)

y-intercept: (0, a)

(a ≠ 0)

Answer 1

The equation of the line passing through a given point with intercepts (a, 0) and (0, b) can be found by substituting the coordinates of the point into the equation x/a + y/b = 1.

Step-by-step explanation:

The equation of a line with intercepts (a, 0) and (0, b) is given by:

x/a + y/b = 1

To write an equation of a line given a point on the line, we substitute the x and y coordinates of the point into the equation.

For the point (−2, 4), the equation becomes:

-2/a + 4/b = 1

This is the equation of the line passing through the point (−2, 4) with intercepts (a, 0) and (0, b).