IB›IB Maths: Analysis and Approaches SL›Mind maps2.1 Equations of straight linesIB Maths: Analysis and Approaches SL: 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 neededGradientm=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2−x1y2−y1Positive slopes up, negative slopes downyyy-intercept: set x=0x = 0x=0xxx-intercept: set y=0y = 0y=0Parallel, perp.Parallel: m1=m2m_1 = m_2m1=m2Perpendicular: m1m2=−1m_1 m_2 = -1m1m2=−1Negative reciprocal: −1m-\frac{1}{m}−m1Perpendicular to 34\frac3443 has gradient −43-\frac43−34Straight linesequations of linesy=mx+cy=mx+cy=mx+cIntersectionsPoint on line if coordinates satisfy itLines meet: solve simultaneouslyShortest distance is perpendicularDistance: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}(x2−x1)2+(y2−y1)2In contextGradient = rise over horizontal distance84 m over 1200 m is 7%In y=mx+cy = mx + cy=mx+c, mmm is the rate of changeccc is the starting valueExam tips3x−4y+12=03x - 4y + 12 = 03x−4y+12=0 has gradient 34\frac3443, not 3Make yyy the subject firstSubtract in the same order top and bottomUse consistent units for gradient