at does the first value in a coordinate pair $(x, y)$ represent?","back":"Horizontal position (the x-coordinate).","mcqOptions":[{"text":"Horizontal position (the x-coordinate).","correct":true,"explanation":"Coordinates are written in the order $(x, y)$, so the first value gives the horizontal position measured along the x-axis."},{"text":"Vertical position (the y-coordinate).","correct":false,"explanation":"The vertical position is given by the second value, called the y-coordinate. The first value is the horizontal position, or x-coordinate."},{"text":"Distance from the origin (the radial coordinate).","correct":false,"explanation":"Distance from the origin must be calculated using both coordinates. The first value alone represents horizontal position and is called the x-coordinate."},{"text":"Quadrant position (the region coordinate).","correct":false,"explanation":"The quadrant depends on the signs of both coordinates, not just the first value. The first value represents horizontal position and is the x-coordinate."}]},{"id":"35f8ef4d-4606-893c-48a3-1ef6072053c3","cardType":"basic","points":1,"front":"At what $x$-value does a line cross the y-axis?","back":"$$x = 0$","mcqOptions":[{"text":"$$x = 0$","correct":true,"explanation":"Every point on the y-axis has an x-coordinate of zero, regardless of its y-coordinate. Therefore, a line crosses the y-axis where $x = 0$."},{"text":"$$y = 0$","correct":false,"explanation":"The condition $y = 0$ describes the x-axis, so it locates an x-intercept rather than a y-intercept. On the y-axis, $x = 0$."},{"text":"$$x = 1$","correct":false,"explanation":"Using 1 confuses the y-axis with a vertical line shifted one unit to the right. The y-axis itself consists of points where $x = 0$."},{"text":"$$x = -1$","correct":false,"explanation":"Using -1 describes a vertical line one unit to the left of the y-axis. A point lies on the y-axis only when $x = 0$."}]},{"id":"cb343c92-8195-c54e-75b9-772a7465f07b","cardType":"basic","points":1,"front":"What is the formula for calculating gradient ($m$)?","back":"$$m = \\frac{\\text{change in } y}{\\text{change in } x}$","mcqOptions":[{"text":"$$m = \\frac{\\text{change in } y}{\\text{change in } x}$","correct":true,"explanation":"Gradient measures vertical change per unit of horizontal change, often called rise over run. Therefore, change in $y$ is divided by change in $x$."},{"text":"$$m = \\frac{\\text{change in } x}{\\text{change in } y}$","correct":false,"explanation":"This reverses rise over run and calculates the reciprocal of the gradient. Gradient is change in $y$ divided by change in $x$."},{"text":"$$m = \\frac{\\text{change in } x + \\text{change in } y}{2}$","correct":false,"explanation":"Averaging the horizontal and vertical changes does not measure a line’s steepness. Gradient is the ratio of change in $y$ to change in $x$."},{"text":"$$m = \\frac{\\text{change in } y}{\\text{change in } x} + c$","correct":false,"explanation":"Adding $c$ confuses the gradient formula with the line equation $y = mx + c$. Gradient alone is change in $y$ divided by change in $x$."}]}]}],"examCountdown":null,"heading":"Equation of a Line","title":"Equation of a Line Flashcards","topbar":{"backHref":"/gcse/maths/ccea/flashcards"},"topicSidebar":"$L33"}]}],"topicId":"cb7f0fe2-32d9-3efc-49c9-b35a3e63941e","walled":"$L34"}],"$L35","$L36"]