Y X Equation of Lines

At the end of this lesson you will be able to: X Write equations of straight lines. Calculate the slope and y – intercept of a line passing through two points.

Intercepts of a line Y-intercept (b): The y-coordinate of the point where the graph of a line crosses the y-axis. (0,b) (a,0) X-intercept (a): The x-coordinate of the point where the graph of a line crosses the x-axis.

Equation of a line An equation of a line is a general rule followed by every point lying on that line. Consider a line l given in this graph. The points (-2, 0), (-1, 1), (0, 2), (1, 3), (2, 4) etc. are some points on the line l. l y-coordinate of each of these points is 2 more than the x-coordinate. In general, if (x, y) is any point on the line, then we may say that, y = x + 2 This is considered as an equation of the line l.

Slope – Intercept form of a line Consider a line with y-intercept ‘b’ and slope ‘m’. (0,b) Let (x, y) be any point on the line (x,y) Then , The equation of the line is ,  

Example 1 Find the equation of the line whose slope is 𝟐 𝟑 and y-intercept 3. Solution:   Y-axis X-axis (0,3)

Example 2 Find the equation of the line passing through the points (0,2) and (5,2) Solution:     Y-axis X-axis (0,2) (5,2)  

Horizontal And Vertical Lines   Y-axis X-axis   (a,b) (a,0)

General Equation Of a Line  

Example 3   Solution:   Y-axis X-axis (3,7) (0,3)  

Example 4   Solution:  

Practice Question