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Find the equation of the line passing through the point of intersection of the given lines
and containing the point (-1, 3).
Solution:
To illustrate the problem, it is better to draw the figure as follows:
For x - 2y = 3,
x - 2y = 3
2y = x - 3
y = ½ x - 3/2
slope (∆y/∆x), m = ½
y-intercept = - 3/2
To trace the graph, plot - 3/2 at the y-axis. This is your first point of the line (0, - 3/2). Next, use the slope to get the second point. From the first point, count 2 units to the right and then 1 unit upward.
For 3x + y = 5,
3x + y = 5
y = - 3x + 5
slope (∆y/∆x), m = - 3
y-intercept = 5
To trace the graph, plot 5 at the y-axis. This is your first point of the line (0, 5). Next, use the slope to get the second point. From the first point, count 1 unit to the left and then 3 units upward.
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| Photo by Math Principles in Everyday Life |
To get their point of intersection, we have to use the two given equations and solve for x and y, we have
Multiply the second equation by 2 and then add in order to eliminate y and solve for the value of x.
Substitute x to either of the two equations,
Therefore, their point of intersection is P(13/7, - 4/7).
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| Photo by Math Principles in Everyday Life |
Finally, we can get the equation of a line using the Two Point Form, we have
