# Question Video: Using the Equation of a Straight Line to Find the π₯-Coordinate of a Point

Find the π₯-coordinate of the point at which the straight line 3π₯ + 9π¦ = 0 cuts the π₯-axis.

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### Video Transcript

Find the π₯-coordinate of the point at which the straight line three π₯ plus nine π¦ equals zero cuts the π₯-axis.

There are lots of ways of approaching this question. Letβs begin by considering the π₯π¦-plane as shown. Any point which cuts the π₯-axis will have a π¦-coordinate equal to zero. This means that we can substitute π¦ equals zero into the equation three π₯ plus nine π¦ equals zero. This gives us three π₯ plus nine multiplied by zero equals zero.

As nine multiplied by zero is zero, we are left with three π₯ is equal to zero. We can then divide both sides of this equation by three. On the left-hand side the threes cancel, and on the right-hand side zero divided by three is zero. The π₯-coordinate of the point at which the straight line three π₯ plus nine π¦ equals zero cuts the π₯-axis is zero.

An alternative method would be to rewrite our equation in slopeβintercept form, π¦ equals ππ₯ plus π, where π is the slope or gradient and π is the π¦-intercept. Subtracting three π₯ from both sides of the original equation, we have nine π¦ is equal to negative three π₯. We can then divide both sides of the equation by nine such that π¦ is equal to negative three-ninths π₯. As both the numerator and denominator of the fraction are divisible by three, this can be rewritten as π¦ is equal to negative one-third π₯.

The equation three π₯ plus nine π¦ equals zero has a slope or gradient equal to negative one-third and a π¦-intercept equal to zero. This linear equation can be drawn on the π₯π¦-plane as shown. As this passes through the origin, this confirms that the π₯-coordinate where the line cuts the π₯-axis is zero.