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. There is a linear relationship between x and y. What is the y-coordinate of the y-intercept of the line in the xy-plane that represents this relationship？
原库参考解析
直线方程・斜率与截距进阶
In the xy-plane, line s passes through the point \( \left(0,\ 0\right) \) and is parallel to the line represented by the equation \( y=42x+6 \). If line s also passes through the point \( \left(4,\ d\right) \), what is the value of d?
原库参考解析
直线方程・斜率与截距进阶
The graph shows the linear relationship between x and y. Which table gives three values of x and their corresponding values of y for this relationship?
原库参考解析
直线方程・斜率与截距挑战
For a linear relationship between x and y, the table gives three values of x and their corresponding values of y. Which equation represents this relationship?
原库参考解析
直线方程・斜率与截距挑战
The function \( f \) is defined by \( f\left(x\right)=98x \). 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
\( j\left(x\right)=mx+132 \)
For the linear function j, m is a constant and j(12) = 18. What is the value of j(10)?
原库参考解析
直线方程・斜率与截距进阶
The function \( f \) is defined by\( f\left(x\right)=\frac{1}{9}x+6 \) . 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
The table shows three values of x and their corresponding values of y. There is a linear relationship between x and y. What is the y-coordinate of the y-intercept of the line in the xy-plane that represents this relationship?
原库参考解析
直线方程・斜率与截距挑战
For the linear function \( t \), the table shows three values of \( x \) and their corresponding values of \( t(x) \). Function \( v \) is defined by \( v(x)=t(x)-4 \) . What is the x-intercept of the graph of \( y=v(x) \) in the xy-plane?
原库参考解析
直线方程・斜率与截距进阶
For a linear relationship between x and y, the table gives three values of x and their corresponding values of y , where t is a constant. Which equation represents this relationship?
原库参考解析
直线方程・斜率与截距挑战
Line p is defined by \( 2y+8x=11 \). Line r is perpendicular to line p in the xy-plane. What is the slope of line r ?
原库参考解析
直线方程・斜率与截距挑战
The function h is defined by \( h(x)=7x-14 \). The graph of \( y=h(x) \) in the xy-plane has an x-intercept at (a, 0) and a y-intercept at (0, b), where a and b are constants. What is the value of \( a+b \)?
原库参考解析
