Answer
A) y = x - 7
Step-by-step
Part 1: Convert to slope-intercept form
The equation -x + y = 5 has to be converted from standard form to slope-intercept form before we can begin solving this problem. The slope-intercept form is y = mx + b, where m is the slope of the line and b is its y-intercept. To convert it, just get y by itself on the left side.
-x + y = 5
y - x = 5
y - x + x = 5 + x
y = 5 + x
y = x + 5
This equation tells us the slope of the line (1) and the line's y-intercept (5)
Part 2: Find the equation of the line that is parallel to y = x + 5 and passes through the point (2, -5)
Parallel lines have equal slopes, so the slope of the line we are looking for will be 1 (or just x). So we can rule out answer choice D because it has a slope of -1 (or -x). To find the y-intercept for the line, we need to find the point where x = 0. We can work backwards with the rise over run method to find this point.
m = rise / run = change in y / change in x
1 = 1 / 1
We can use this information to perform a series of transformations (down 1 unit then left 1 unit) that will bring us to the y-intercept.
(2, -5) --> (1, -6)
(1, -6) --> (0, -7)
The point (0, -7) has an x-coordinate of 0, which means that the line intercepts the y-axis at this point.
The slope of the desired line is 1 and its y-intercept is -7.
Part 3: Substitute into the slope-intercept equation
y = mx + b
m = slope = 1 = x
b = y-intercept = -7
y = x - 7
The answer is false because it crosses together and parallel would have the same slope!
Hope this helps!!
Answer:
(0,0), (0,1), (1,2), (1,3)
Step-by-step explanation:
To determine what makes ordered pairs a function, we have to make sure each input (x) goes to exactly one output (y).
The reason this is the answer is that each input doesn't have exactly one output. (0 goes to 0 and 1. 1 goes to 2 and 3).