The equation of a line can be found using different forms depending on the information available about the line. The most common is the slope-intercept form: y=mx+by=mx+by=mx+b where mmm is the slope of the line (how steep it is), and bbb is the y-intercept (the value of yyy when x=0x=0x=0). Here are the main methods to find the equation of a line:
- If you know the slope mmm and the y-intercept bbb, just substitute them into y=mx+by=mx+by=mx+b.
- If you know the slope mmm and one point(x1,y1)(x_1,y_1)(x1,y1) on the line, use the point-slope form:
y−y1=m(x−x1)y-y_1=m(x-x_1)y−y1=m(x−x1)
- If you know two points(x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2), first find the slope using:
m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
then use the point-slope form with one of the points.
- If you know the x-intercept aaa and y-intercept bbb, use the intercept form:
xa+yb=1\frac{x}{a}+\frac{y}{b}=1ax+by=1
Summary of key formulas and steps:
- Find slope m=ΔyΔxm=\frac{\Delta y}{\Delta x}m=ΔxΔy if needed.
- Use a known point and slope in point-slope form.
- Rearrange to slope-intercept form y=mx+by=mx+by=mx+b if desired.
This process allows finding the line equation given points, slope, or intercepts.
