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・斜率与截距挑战
In the xy-plane, line k and line l are perpendicular and intersect at the point (7, 5). If line k is defined by the equation \( y=mx+b, \)where m and b are constants and \( m>1 \) . Which of the following points lies on line l?
原库参考解析
直线方程・斜率与截距挑战
The function \( f \) is defined by \( f\left(x\right)=6x-\frac{1}{8} \) .What is the y-intercept of the graph of \( y=f\left(x\right) \) in the xy-plane?
原库参考解析
直线方程・斜率与截距挑战
The graph of the linear function \( f \) is shown, where \( y=f(x) \) . Which equation defines \( f \) ?
原库参考解析
直线方程・斜率与截距挑战
In the xy-plane, line s is parallel to line t. Line s is defined by \( y+16=7x \) . What is the slope of line t?
原库参考解析
直线方程・斜率与截距进阶
\( f\left(x\right)=7x+b \)
For the linear function \( f \), b is a constant and \( f(8)=56 \) . What is the value of b?
原库参考解析
直线方程・斜率与截距挑战
Line s in the xy-plane is defined by \( 6x+2y=0 \) . Line t is perpendicular to line s and passes through the points \( (7,\ 0) \) and \( (k,\ \frac{4}{3}) \) . What is the value of k?
原库参考解析
直线方程・斜率与截距挑战
The table shows two values of x and their corresponding values of h(x) for the linear function h. Which equation defines h?
原库参考解析
直线方程・斜率与截距挑战
For the linear function f, \( f\left(2\right)=3 \)and \( f\left(6\right)=5 \). Which equation defines f?
原库参考解析
直线方程・斜率与截距挑战
Line r is defined by the equation 6x-5y=9. Line s is parallel to line r in the xy-plane. What is the slope of line s?
原库参考解析
直线方程・斜率与截距挑战
The function \( f \)is defined by \( f\left(x\right)=\frac{4}{11}x \). What is the slope of the graph of \( y=f\left(x\right) \) 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 \( g \), the table shows three values of \( x \) and their corresponding values of \( g(x) \). Function \( g \) is defined by \( g(x)=ax+b \), where \( a \) and \( b \) are constants. What is the value of \( a+b? \)
原库参考解析
直线方程・斜率与截距挑战
The table shows four values of \( x \) and their corresponding values of \( y \). The linear relationship between \( x \) and \( y \) can be represented by the equation \( 2x+By=C \), where \( B \) and \( C \) are constants. What is the value of C?
原库参考解析
