Video Transcript
Find the coordinates of the intersection point between a straight line represented by the equation three 𝑥 minus nine 𝑦 equals negative nine and the 𝑦-axis.
Let’s begin by considering the 𝑥𝑦-coordinate plane as shown. We know that any point that intersects the 𝑦-axis will have an 𝑥-coordinate equal to zero. This means that we can substitute 𝑥 equals zero into our equation three 𝑥 minus nine 𝑦 is equal to negative nine. As three multiplied by zero is zero, this simplifies to negative nine 𝑦 is equal to negative nine. We can then divide both sides of this equation by negative nine such that 𝑦 is equal to one. As 𝑥 is equal to zero and 𝑦 is equal to one, the coordinates of the intersection point between the straight line three 𝑥 minus nine 𝑦 equals negative nine and the 𝑦-axis is zero, one.
An alternative method here is to rewrite our equation in slope–intercept form. This can be written 𝑦 is equal to 𝑚𝑥 plus 𝑏, where 𝑚 is the slope or gradient and 𝑏 is the 𝑦-intercept. Subtracting three 𝑥 from both sides of our equation gives us negative nine 𝑦 is equal to negative three 𝑥 minus nine. We can then divide both sides of our equation by negative nine, giving us 𝑦 is equal to negative three 𝑥 minus nine all divided by negative nine. As negative three divided by negative nine is one-third and negative nine divided by negative nine is one, this simplifies to 𝑦 is equal to one-third 𝑥 plus one. This equation has a slope or gradient equal to one-third and a 𝑦-intercept equal to one.
The equation three 𝑥 minus nine 𝑦 equals negative nine can be drawn as shown. This straight line intersects the 𝑦-axis at the point with coordinates zero, one. This confirms that our original answer was correct.
