3-41a5-8971-5bdddb2cbb6f","cardType":"basic","front":"In the straight-line equation $y=mx+c$, what does $m$ represent?","back":"The gradient (steepness and direction).","points":1},{"id":"fdbc68d2-9896-45cd-8e27-2b6b3bc8b566","cardType":"basic","front":"In the straight-line equation $y=mx+c$, what does $c$ represent?","back":"The y-intercept (where the line crosses the y-axis).","points":1},{"id":"1dd39706-88a8-4504-b1f4-b2efbecd3281","cardType":"basic","front":"What is the gradient of the line $y=5-x$?","back":"$$-1$","points":1},{"id":"79393b1c-e3a9-42d3-89a4-d27c4a40d320","cardType":"basic","front":"What is the coordinate of the y-intercept for the line $y=4x-6$?","back":"$$(0,-6)$","points":2},{"id":"da730c85-8821-444b-ac38-8b2259724b29","cardType":"basic","front":"When rearranging an equation into the form $y=mx+c$, what must you do when dividing by the coefficient of $y$?","back":"Divide every term on the other side of the equation.","points":1},{"id":"189aab52-96ed-48c5-b1c8-a6395886913d","cardType":"basic","front":"What is the gradient of a line with equation $3y = 12x + 9$?","back":"$$4$ (divide both sides by 3).","points":2},{"id":"d52ea23c-1681-43bf-940c-77637fc98aaa","cardType":"basic","front":"If a line passes through $(0,2)$ and $(3,8)$, what is the y-intercept ($c$)?","back":"$$2$","points":1},{"id":"6d345edb-08a7-42dd-a3aa-312571e1571d","cardType":"basic","front":"How can you tell if two lines are parallel from their equations?","back":"They have the same gradient ($m$).","points":1},{"id":"620076e6-6a78-4fb3-b1bf-1a258aecc2f8","cardType":"basic","front":"Write the equation of a line parallel to $y=-3x+4$ that passes through $(0,7)$.","back":"$$y=-3x+7$","points":2},{"id":"70b47b5a-d2fc-48aa-9e27-6bdd8ba83775","cardType":"basic","front":"What is the general equation for a horizontal line?","back":"$$y=c$ (where $c$ is a constant).","points":1},{"id":"0e572fe5-ef49-4516-957c-c9d8252ba201","cardType":"basic","front":"Identify the gradient and y-intercept for the line $y=7-2x$.","back":"

Gradient: -2
y-intercept: 7

","points":2},{"id":"7932c1e7-4c9a-4747-a44a-e4ced39d5f5a","cardType":"basic","front":"What is the gradient of a line that slopes downwards from left to right?","back":"A negative gradient.","points":1},{"id":"e4d93baa-326d-457a-997d-489355adae5e","cardType":"basic","front":"What are the two most important clues to look for when matching a graph to an equation?","back":"

The direction of the slope (positive or negative)
The y-intercept value

","points":2},{"id":"c01e0d3f-8fd3-401a-832b-a2d782ca053b","cardType":"basic","front":"Calculate the gradient of a line passing through $(0,5)$ and $(2,-1)$.","back":"$$-3$ (Calculation: $\\frac{-1-5}{2-0} = \\frac{-6}{2}$)","points":2},{"id":"e5eebc3c-f48c-4d55-b3bd-67a4e29ccb06","cardType":"basic","front":"Rearrange $x+4y=12$ to make $y$ the subject.","back":"$$y = -\\frac{1}{4}x + 3$","points":2}]}],"examCountdown":null,"formulaUrl":null,"intro":"$L3d","title":"Equation of a Line Flashcards","topicSidebar":"$L3e"}]}],"topicId":"8849f02d-00e5-499c-9d41-0e17db0f3354","walled":"$L3f"}],"$L40"]