Final answer:
To write two different linear equations containing the point (5, 12), first choose different slopes for each equation, then solve for the y-intercept by substituting the given point and the chosen slope into the linear equation form y = mx + b. Examples with slopes of 2 and -1 result in the equations y = 2x + 2 and y = -1x + 17, respectively.
Step-by-step explanation:
To write two different linear equations that contain the point (5, 12), we can use different slopes (m). The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we plug in the point (5, 12) into the equation and solve for b, after deciding on a value for m.
Example 1:
Let's choose a slope of 2. Then the equation becomes y = 2x + b. Substituting the point (5, 12) gives us 12 = 2(5) + b, which simplifies to b = 2. So, one equation that has the point (5, 12) is:
y = 2x + 2
Example 2:
Now, let's choose a different slope, say -1. Then the equation becomes y = -1x + b. Substituting the point (5, 12) into this equation gives us 12 = -1(5) + b, which simplifies to b = 17. So, another equation that contains the point (5, 12) is:
y = -1x + 17