Question

Find the equation of a line with $$x$$-intercept $$= 5$$ and passing through the point $$(4, -3)$$.

[Hint. The line passes through the points A(5, 0) and B(4, –3).]

Answer 1

Since the $$x$$-intercept is $$5$$, the line passes through the point $$(5, 0)$$.

The line also passes through $$(4, -3)$$.

Slope of the line: $$m = \frac{-3 - 0}{4 - 5}$$

$$= \frac{-3}{-1}$$

$$= 3$$

Using the point-slope form with $$(5, 0)$$: 

$$y - 0 = 3(x - 5)$$

$$y = 3x - 15$$

$$3x - y - 15 = 0$$

Thus, the equation of the line is $$3x - y - 15 = 0$$.