Question:
The x-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $(1, 2)$ is :
The x-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $(1, 2)$ is :
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The x-intercept is simply the x-value where the line crosses the x-axis, which is why we always set $y = 0$. Finding the full equation first is the most reliable method.
Updated On: Jun 4, 2026
- $-1$
- $-2$
- $1$
- $3$
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
We need to find the x-intercept of a straight line that passes through two given coordinate points.
Step 2: Key Formula or Approach:
First, find the slope ($m$) of the line using $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Then, use the point-slope form $y - y_1 = m(x - x_1)$ to find the linear equation.
Finally, substitute $y = 0$ to find the x-intercept.
Step 3: Detailed Explanation:
Given points: $(x_1, y_1) = \left(-\frac{1}{2}, 1\right)$ and $(x_2, y_2) = (1, 2)$.
Calculate the slope $m$:
$$m = \frac{2 - 1}{1 - \left(-\frac{1}{2}\right)} = \frac{1}{\frac{3}{2}} = \frac{2}{3}$$ Use the point-slope equation with the point $(1, 2)$:
$$y - 2 = \frac{2}{3}(x - 1)$$ Multiply by 3 to clear the fraction:
$$3y - 6 = 2x - 2 \implies 2x - 3y + 4 = 0$$ To find the x-intercept, set $y = 0$:
$$2x - 3(0) + 4 = 0 \implies 2x = -4 \implies x = -2$$
Step 4: Final Answer:
The x-intercept is $-2$, matching option (B).
We need to find the x-intercept of a straight line that passes through two given coordinate points.
Step 2: Key Formula or Approach:
First, find the slope ($m$) of the line using $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Then, use the point-slope form $y - y_1 = m(x - x_1)$ to find the linear equation.
Finally, substitute $y = 0$ to find the x-intercept.
Step 3: Detailed Explanation:
Given points: $(x_1, y_1) = \left(-\frac{1}{2}, 1\right)$ and $(x_2, y_2) = (1, 2)$.
Calculate the slope $m$:
$$m = \frac{2 - 1}{1 - \left(-\frac{1}{2}\right)} = \frac{1}{\frac{3}{2}} = \frac{2}{3}$$ Use the point-slope equation with the point $(1, 2)$:
$$y - 2 = \frac{2}{3}(x - 1)$$ Multiply by 3 to clear the fraction:
$$3y - 6 = 2x - 2 \implies 2x - 3y + 4 = 0$$ To find the x-intercept, set $y = 0$:
$$2x - 3(0) + 4 = 0 \implies 2x = -4 \implies x = -2$$
Step 4: Final Answer:
The x-intercept is $-2$, matching option (B).
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