SLOPE,+INTERCEPTS

There are two popular forms of a linear equation: standard form and slope intercept form. STANDARD FORM: AX + BY = C   ·  A, B, and C are integral and A > 0 · 13x + 7y = 20 is in standard form · -2/3x + 4/5y = 173 isn’t in standard form because A and B aren’t integral and A isn’t greater than zero SLOPE INTERCEPT FORM: y = mx + b  ·  2y = 4x + 10 isn’t in slope intercept form because the equation isn’t solved for y  ·  Y = 2x + 5 is in slope intercept form INTERCEPTS When a linear equation contains both variables, it will intersect the x axis and the y axis. The points of intersection with the axis are called intercepts. A vertical line will only have an x intercept and its equation will only contain an x. A horizontal line will only have a y intercept and its equation will only contain a y. Slope is the steepness or slant of the line. There are 4 positions a line can be in.  Vertical <span style="font-size: 120%; font-family: Impact,Charcoal,sans-serif; color: rgb(31, 60, 244)"> Horizontal

<span style="font-family: Impact,Charcoal,sans-serif; color: rgb(14, 47, 241)"> <span style="font-size: 120%; font-family: Impact,Charcoal,sans-serif; color: rgb(0, 0, 0)"><span style="font-family: Impact,Charcoal,sans-serif; color: rgb(12, 38, 228)">Positive Slope <span style="font-size: 130%; font-family: Impact,Charcoal,sans-serif; color: rgb(6, 30, 239)"><span style="font-size: 120%; font-family: Impact,Charcoal,sans-serif; color: rgb(31, 60, 244)">Negative Slope



There are three ways to determine the slope of a line. 1. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> By graph ( Rise/Run) 2. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> By equation ·<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> Standard form: Slope is –A/B ·<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> Slope intercept form: Slope is m  3. <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> By two points: (y2-y1)/(x2-x1)