With geometry; will give how would i solve a problem such as the following: write an equation of the line that is parallel to -x + y = 5 and passes through the point (2, -5). a) y = x - 7 b) y = x - 5 c) y = x - 3 d) y = -x - 3

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

here the number -5 is all of the following except a rational number.

step-by-step explanation:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: