The statement is false. A linear equation in two variables (like y = mx + b) typically produces a straight line when graphed on a coordinate plane.
To understand the x-intercepts of a linear equation, we need to determine where the line crosses the x-axis. The x-intercept occurs when y = 0. To find the x-intercept, we can set y to 0 in the equation of the line:
0 = mx + b
Rearranging this gives:
mx = -b
x = -b/m (assuming m ≠ 0)
From this, we can see that:
- If the slope (m) is not zero, the line will have exactly one x-intercept.
- If the slope (m) is zero, the line is horizontal (y = b). In this case, it will not intersect the x-axis at all unless b = 0, in which case, the line would lay along the x-axis, and every point on the x-axis can be considered an intercept.
Thus, the only situations for a linear graph regarding x-intercepts are:
- One x-intercept (when the line is not horizontal).
- No x-intercept (when the line is horizontal and not at y = 0).
In conclusion, a linear equation’s graph cannot have