find an equation

Question

Find an equation of the line that has a slope of -1 and a y intercept of 7. Write your answer in the form .

Answer 1

m = -1

b = 7

y = mx + b

y = -x + 7

Answer 2

The y-intercept is the point (0,7) where the line crosses the y-axis

The slope = m = -1 is the ratio of the change in y over the change in x moving along the line from one point to another. (y-7)/(x-0) = -1. It's called sometimes the "rise over the run," or how y changes as x changes.

(y-7)/(x-0) is the change in y as x changes moving from the given point, the y-intercept, (0,7).

(y-7)/(x-0)=-1 can be simplified and rewritten in y=mx+b form

(y-7)/x=-1 x-0=x

y-7=(-1)(x)=-x multiply both sides by x

y=-x+7 add 7 to both sides

Or you could have just plugged in the m and b values, -1 and 7, substituting directly into y=mx+b

a negative slope means the line goes downhill, as it goes left to right.

negative one slope means it goes downhill at a 45 degree angle, going down 1 as it goes to the right 1, a decrease of one unit of y as x increases one unit

Answer 3

The slope-intercept form of a linear equation is y = mx + b, where m represent the slope and b represents the y-intercept. Therefore, the equation of the line that has a slope of -1 and a y-intercept of 7 is y = -x + 7.