The Importance of Education- English Paragraph

General Equation of a Straight Line

1. Standard form: $𝑎𝑥+𝑏𝑦+𝑐=0$ where $𝑎$, $𝑏$, and $𝑐$ are constants.

Slope-Intercept Form

2. Slope-Intercept form: $𝑦=𝑚𝑥+𝑐$ where $𝑚$ is the slope and $𝑐$ is the y-intercept.

Point-Slope Form

3. Point-Slope form: $𝑦-{𝑦}_1=𝑚(𝑥-{𝑥}_1)$ where $𝑚$ is the slope and $({𝑥}_1,{𝑦}_1)$ is a point on the line.

Intercept Form

4. Intercept form: $\frac{𝑥}{𝑎}+\frac{𝑦}{𝑏}=1$ where $𝑎$ and $𝑏$ are the x-intercept and y-intercept, respectively.

Two-Point Form

5. Two-Point form: $𝑦-{𝑦}_1=\frac{{𝑦}_2-{𝑦}_1}{{𝑥}_2-{𝑥}_1}(𝑥-{𝑥}_1)$ where $({𝑥}_1,{𝑦}_1)$ and $({𝑥}_2,{𝑦}_2)$ are two points on the line.

Slope Calculation

6. Slope of a line passing through two points: $𝑚=\frac{{𝑦}_2-{𝑦}_1}{{𝑥}_2-{𝑥}_1}$ where $({𝑥}_1,{𝑦}_1)$ and $({𝑥}_2,{𝑦}_2)$ are the coordinates of the two points.

Distance Formula

7. Distance between two points: $𝑑=\sqrt{({𝑥}_2-{𝑥}_1{)}^2+({𝑦}_2-{𝑦}_1{)}^2}$ where $({𝑥}_1,{𝑦}_1)$ and $({𝑥}_2,{𝑦}_2)$ are the coordinates of the two points.

Distance from a Point to a Line

8. Distance from a point to a line: $𝑑=\frac{\mathrm{\mid }𝑎{𝑥}_1+𝑏{𝑦}_1+𝑐\mathrm{\mid }}{\sqrt{{𝑎}^2+{𝑏}^2}}$ where $𝑎𝑥+𝑏𝑦+𝑐=0$ is the equation of the line and $({𝑥}_1,{𝑦}_1)$ is the point.