Converting Slope-Intercept Form to Standard Form

Converting Slope-Intercept Form to Standard Form

Slope-Intercept Form

• The slope-intercept form of a linear equation is given by: $y = mx + b$, where:

  • $m$ represents the slope of the line.

  • $b$ represents the y-intercept (the point where the line crosses the y-axis).

Standard Form

• The standard form of a linear equation is given by: $Ax + By = C$, where:

  • $A$, $B$, and $C$ are constants.

  • $A$ and $B$ cannot both be zero.

Converting from Slope-Intercept to Standard Form

1. Given Equation: Start with an equation in slope-intercept form, such as $y = 2.6x + 2$. It seems there's a typo, and it should likely be a complete equation. Assuming it is $y = -2x - 3$.

2. Rearrange the Equation: The goal is to rearrange the equation so that the terms with $x$ and $y$ are on one side, and the constant is on the other side.

   • For the equation $y = -2x - 3$, add $2x$ to both sides:
     $y + 2x = -2x - 3 + 2x$
     $2x + y = -3$

   • Now the equation is in standard form: $2x + y = -3$, where $A = 2$, $B = 1$, and $C = -3$.

Example

• Given: $2y = -x + 12$

• Rearrange to standard form: $x + 2y = 12$, where $A = 1$, $B = 2$, and $C = 12$.

Finding x and y Intercepts

• To find the x-intercept, set $y = 0$ and solve for $x$.

• To find the y-intercept, set $x = 0$ and solve for $y$.

Example: Using $x + 2y = 12$

• Finding the x-intercept:

  • Set $y = 0$: $x + 2(0) = 12$

  • Simplify: $x + 0 = 12$

  • Therefore, $x = 12$. The x-intercept is at the point $(12, 0)$.

It seems the last part of the transcript $1=-10x+1/12$ and $110x+y 12$, $2x+1=$, $2$ are incomplete or out of context. Disregarding for now.