The point where the graphs of two equations intersect has y -coordinate 2. One equation is y=−3x+5Find the other equation if its graph has a slope of 1.
The y-coordinate of the intersection point is 2. Therefore, substituting this into the first equation, we can write it as:
2 = -3x + 5
Rearranging the equation to solve for x, we have:
3x = 5 - 2
3x = 3
x = 1
So the x-coordinate of the intersection point is 1.
The other equation has a slope of 1. We can write it in slope-intercept form as:
y = mx + b
Since the intersection point is (1, 2), we can substitute these values into the equation to solve for the y-intercept, b:
2 = 1(1) + b
2 = 1 + b
b = 1
Therefore, the other equation with a slope of 1 is y = x + 1.