Question

a straight line has an x intercept -2 and passes through the point (-4,6) Find its equation

Answer 1

The x-intercept is the point where the line crosses the x-axis. That point has a y-coordinate of 0. The coordinates of the x-intercept are (-2, 0). You are also given point (-4, 6), so you have two points on the line.

You can use the two-point form of the equation of a line to find its equation.
The two points are $(x_1, y_1)$ and $(x_2, y_2)$

$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

$y - 0 = \dfrac{6 - 0}{-4 - (-2)}(x - (-2))$

$y = \dfrac{6}{-2}(x + 2)$

$y = -3(x + 2)$

$y = -3x - 6$