Find conditions on the slope of a line through (9, 4) such that the x-intercept is negative and the slope is greater than its y-intercept. 2/5 < m < 4/9 m < 2/5 or m &g…

Question

Find conditions on the slope of a line through (9, 4) such that the x-intercept is negative and the slope is greater than its y-intercept. 2/5 < m < 4/9 m < 2/5 or m > 4/9 9/5 < m < 9/4 m < 9/5 or m > 9/4 Not enough information

Answer 1

9/5 < m < 9/4

Explanation:

The conditions are:

• The line passes through (9,4)

• x-intercept is negative

• The slope (m) is greater than its y-intercept

If we take a point like (-1,0)

Slope (m) = change in y ÷ change in x =
`(0 - 9)/(-1 - 4) = (-9)/(-5)` = 9/5

This point satisfies the conditions above since;

1. The line passes through points (9,0) and (-1,0)
2. The x-intercept is negative i.e -1
3. The y-intercept is 0 and the slope which equals 9/5 is greater than 0

From the choices given;

we can say that:

m > 9/5 and m < 9/4

And can be expressed as;

9/5 < m < 9/4