Question

X-intercept is -2, y-intercept is -4Find the equation of a line with the x and y intercepts.

Answer 1

Equation of a line in slope-intercept form

`y=mx+b`

where m is the slope and the point (0, b) is the y-intercept.

The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

`m=(y_2-y_1)/(x_2-x_1)`

Given that the x-intercept of this line is -2, then the line passes through (-2, 0), and given that the y-intercept is -4. then the line passes through (0, -4), then its slope is:

`m=(-4-0)/(0-(-2))=(-4)/(2)=-2`

Substituting with m = -2 and b = -4 into the general equation, we get:

`\begin{gathered} y=(-2)x+(-4) \\ y=-2x-4 \end{gathered}`