IB›IB Maths: Analysis and Approaches HL›Mind maps2.1 Equations of straight linesIB Maths: Analysis and Approaches HL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsThree formsGradient–intercept: y=mx+cy = mx + cy=mx+cGeneral: ax+by+d=0ax + by + d = 0ax+by+d=0Point–gradient: y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1=m(x−x1)Rearrange between forms as neededGradient, interceptsm=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2−x1y2−y1Positive gradient slopes up, negative slopes downyyy-intercept: set x=0x = 0x=0xxx-intercept: set y=0y = 0y=0Straight linesequations of linesy=mx+cy=mx+cy=mx+cParallel, perpendicularParallel: m1=m2m_1 = m_2m1=m2Perpendicular: m1m2=−1m_1 m_2 = -1m1m2=−1Perpendicular gradient is the negative reciprocalPerpendicular to 34\frac3443 has gradient −43-\frac43−34Meeting pointsA point is on a line if it satisfies the equationLines meet: solve simultaneouslyShortest distance is along the perpendicularDistance =(x2−x1)2+(y2−y1)2= \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}=(x2−x1)2+(y2−y1)2Exam tips3x−4y+12=03x - 4y + 12 = 03x−4y+12=0 has gradient 34\frac3443, not 3Same order of subtraction on top and bottomUse horizontal distance and matching unitsPerpendicular proof: show product is −1-1−1, say so