The x-intercept of a line is the point where the graph of the line crosses the x-axis. At this point, the y-coordinate is always zero. To find the x-intercept from the equation of a line, you set y=0y=0y=0 in the equation and solve for xxx. Here are some common forms of the line equation and how to find the x-intercept:
- For the general form ax+by+c=0ax+by+c=0ax+by+c=0, substitute y=0y=0y=0:
ax+c=0 ⟹ x=−caax+c=0\implies x=-\frac{c}{a}ax+c=0⟹x=−ac
- For the slope-intercept form y=mx+by=mx+by=mx+b, substitute y=0y=0y=0:
0=mx+b ⟹ x=−bm0=mx+b\implies x=-\frac{b}{m}0=mx+b⟹x=−mb
- For the point-slope form y−y1=m(x−x1)y-y_1=m(x-x_1)y−y1=m(x−x1), substitute y=0y=0y=0 and solve for xxx:
0−y1=m(x−x1) ⟹ x=x1−y1m0-y_1=m(x-x_1)\implies x=x_1-\frac{y_1}{m}0−y1=m(x−x1)⟹x=x1−my1
- For the intercept form xa+yb=1\frac{x}{a}+\frac{y}{b}=1ax+by=1, the x-intercept is simply aaa because when y=0y=0y=0, x=ax=ax=a.
In summary, to find the x-intercept, always substitute y=0y=0y=0 in the equation of the line and solve for xxx. The x-intercept is the xxx-value at that point, and the coordinate will be (x,0)(x,0)(x,0).
