Find the equation of the line: with x-intercept 5 and y- intercept -7

Answer 1

When you know the x-intercept [ the point (a,0) where y=0 ] and the y=intercept [the point (0,b) where x=0 ], you may use the two-intercept form of the equation of a line:

x/a + y/b = 1

x/5 + y/(-7) = 1

Put this into other forms:

7x - 5y = 35 [Standard Format]

y = (7/5)x - 7 [slope-intercept form]

. . .

Answer 2

point slope formula is y=mx+b m is the slope b is the y intercept = -7

the slope is rise over the run, how many do you go up or down as you go to the right Go to the right by 5 and you go up 7, so m=7/5

y=(7/5)x-7

or remove the fraction to get 5y=7x-35

or 7x-5y=35 check the answer with two points, the x-intercept is (5,0) plug it in

to get 7(5) - 0 = 35

then plug in the y intercept of (0,-7) to get 0-5(-7) =35

Another way to do this is to use two expressions for the slope and set them equal

or [y-(0)/(x-5)] = (y-(-7))/(x-0)

cross multiply to get

(x-5)(y+7)= xy

expand

xy +7x -5y -35 = xy

xy cancels out

leaving

7x-5y =35

Answer 3

With an x-intercept of (5,0) and a y-intercept of (0,-7), obtain the slope of the line m: m = (-7 − 0)/(0 − 5) or m is equal to -7/-5 or 7/5.

Using the slope-intercept form of a line equation (y = mx + b) where b is the ordinate of the y-intercept given (-7) and m is the slope of 7/5, obtain y = (7/5)x + -7 or y = (7/5)x − 7.

Ensure that this equation works for (5,0) and for (0,-7):

0 = (7/5)(5) − 7 or 0 does equal 7 − 7.

-7 = (7/5)(0) − 7 or -7 does equal 0 − 7.

The equation underlined is valid.