这部分需要会什么？
- 由两点或图象求斜率
- 识别斜截式、点斜式和一般式
- 解释截距并判断平行与垂直
核心概念与公式
两点 \((x_1,y_1),(x_2,y_2)\) 且 \(x_1\ne x_2\) 时，斜率 \(m=(y_2-y_1)/(x_2-x_1)\)。它表示横坐标每增加 1，纵坐标的变化量。直线常写成 \(y=mx+b\) 或 \(y-y_1=m(x-x_1)\)。
\(y\) 截距为 \((0,b)\)；求 \(x\) 截距需令 \(y=0\)。不同非竖直平行线斜率相同；两条非竖直直线垂直时 \(m_1m_2=-1\)。竖直线 \(x=c\) 的斜率不存在，它与水平线垂直。
做题时怎样使用
- 有两点先求斜率；有一点和斜率优先用点斜式
- 需要截距时分别令另一个坐标为零
- 把所得直线代回给定点，检查坐标和单位
容易混淆的地方
斜率分子与分母必须采用相同的点的顺序。截距是坐标轴上的位置；\(y\) 截距的纵坐标才是式中的 \(b\)。
用一个例题串起方法
知识点教学例题一条直线经过 \((2,7)\) 与 \((5,16)\)。求它的方程及 \(y\) 截距。
展开解题思路 ＋
\(m=(16-7)/(5-2)=3\)。用点斜式得 \(y-7=3(x-2)\)，即 \(y=3x+1\)。因此 \(y\) 截距为 \((0,1)\)。
本知识点题库
先独立作答，再查看答案与解析。
直线方程・斜率与截距进阶
What is the slope of the graph of 14x - 2y = -42 in the xy-plane?
原库参考解析
直线方程・斜率与截距进阶
Line k is shown in the xy-plane. Line n (not shown) is perpendicular to line k and passes through the point (3,8). Which equation defines line n?
原库参考解析
直线方程・斜率与截距进阶
The function g is defined by g(x) =\( \frac{3}{7}x \) - 15.What is the x-coordinate of the x-intercept of the graph of y = g(x ) in the xy-plane?
原库参考解析
直线方程・斜率与截距挑战
For the linear function f, the graph of y = f(x) in the xy-plane has a slope of \( \frac{3}{4} \) and passes through the point (12,10). which equation defines f ?
原库参考解析
直线方程・斜率与截距进阶
Line k has a slope of 2 and a y-intercept of (0, 18). What is the x-coordinate of the x-intercept of line k?
原库参考解析
直线方程・斜率与截距进阶
Line q in the xy-plane has a slope of -2 and passes through the point (0, 12). Which equation defines line q?
原库参考解析
直线方程・斜率与截距挑战
When the linear function h is graphed in the xy-plane, where y= h(x), its slope is -2. If h(4)= 3, which equation defines h?
原库参考解析
直线方程・斜率与截距进阶
Line t in the xy-plane has a slope of \( \frac{1}{8} \) and passes through the point (40, -7). which equation defines line t ?
原库参考解析
直线方程・斜率与截距挑战
The function f is defined by f(x) =ax＋b, where a and b are constants. In the xy-plane, the graph of y = f(x ) has an x-intercept at (2,0) and a y-intercept at (0,-24). What is the value of b?
原库参考解析
直线方程・斜率与截距进阶
What is the slope of the graph of \( y=\frac{1}{4}\left(39x+15\right)+8x \) in the \( xy \)-plane?
原库参考解析
直线方程・斜率与截距进阶
For the linear function f, the graph of y=f(x) in the xy-plane passes through the points (0, 2) and (3, 3). What is the slope of y=f(x).
原库参考解析
直线方程・斜率与截距进阶
What is the y-intercept of the graph of 3x+2y=96 in the xy-plane?
原库参考解析
