Q11. - Algebra 1

Question

Write an equation of the line that passes through the point $\left(0,0\right)$ and has a slope $-4$.

A. $y=x-4$

B. $y=x+4$

C. $y=-4x$

D. $y=4-x$

Step-by-Step Solution

Answer

The equation of the straight line for the given condition is $y=-4x$. Option (C) is correct.

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$ is the slope of the straight line and $c$ is the $y$-intercept of the equation.

Step 2. State the equation of a line slope-point form.

The standard form of slope and point form of the straight line is $y-y_1=m\left(x-x_1\right)$

Here $m$ is the slope of the straight line and is the point from which the straight line passes.

$$\begin{gathered} \left(x_1,y_1\right)=\left(0,0\right) \\ m=-4 \end{gathered}$$

Step 3. Substitute the values to get the required equation.

Substitute the above values in the equation $y-y_1=m\left(x-x_1\right)$

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-0=-4\left(x-0\right) \\ y=-4x \end{gathered}$$

The equation of the straight line is $y=-4x$. Option (C) is correct.