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
The table shows three values of x and their corresponding values of y. The linear relationship between x and y can be represented by an equation written in the form \( Ax+By=C \), where A, B, and C are constants, What is the value of \( \frac{A}{B} \)?
原库参考解析
直线方程・斜率与截距挑战
For the linear function h, \( h\left(0\right)=0 \) and \( h\left(11\right)=5 \). 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 \( \frac{1}{4} \) and passes through the point (\( 12,−8 \)). Which equation defines line t?
原库参考解析
直线方程・斜率与截距进阶
The linear function g is defined by \( g\left(x\right)=b-18x \), where b is a constant. If \( g\left(c+6\right)=\frac{c}{5} \), where c is a constant, which of the following expressions represents 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 line shown?
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 \( 48x-6y=-32 \) in the xy-plane?
原库参考解析
直线方程・斜率与截距进阶
Line r in the xy-plane has a slope of \( −8 \) and passes through the point \( \left(0,\ 60\right) \). Which equation defines line r ?
原库参考解析
直线方程・斜率与截距进阶
\( h\left(x\right)=x+b \)
For the linear function h , b is a constant and \( h\left(0\right)=26 \). What is the value of b ?
原库参考解析
直线方程・斜率与截距挑战
Line k is defined by \( y=3x-2 \). Line j is parallel to line k in the xy-plane and passes through the point (0, 1) .Which equation defines line j?
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 j (not shown) is perpendicular to line k. What is the slope of line j?
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 \( y=f\left(x\right) \) in the xy-plane has a slope of \( \frac{1}{3} \)and passes through the point \( \left(0,\ 7\right) \). Which equation defines \( f \)?
原库参考解析
直线方程・斜率与截距进阶
\( 5x-4y=-60 \)
For the given equation, which table gives three values of x and their corresponding values of y?
原库参考解析
