Question

What are the intercepts of : `5y= 7x - 19`?

Answer 1

`x = 19/7`

`y = -19/5`

Explanation:

To find the `x`-intercept, we set `y` equal to `0` and solve:

`5 xx 0 = 7 xx x - 19`

`19 = 7x`

`x = 19/7`

Now we solve for when `x = 0` to get the `y`-intercept:

`5 y = 7 xx 0 - 19`

`5 y = -19`

`y = -19/5`

To check our work, let''s graph the equation and make sure our intercepts are correct

graph{5y = 7x-19}

Yep, we were right!

Answer 2

`x` intercept `= 19/7, y` intercept `= -19/5`

Explanation:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

Given equation is `5y = 7x - 19`

To find x intercept : when y = 0,

`7x - 19 = (5*0) = 0`

`7x = 19` or `x = 19/7`

To find y intercept : when x = 0,

`(7*0) - 19 = 5y`

`5y = -19` or `y = -19/5`

`color(purple)(y = (7x-19) / 5`
graph{(7x - 19) / 5 [-10, 10, -5, 5]}

Answer 3

The x-intercept is `(19/7,0)` or `~~(2.714,0)`.

The y-intercept is `(0,-19/5)` or `(0,-3.8)`.

Explanation:

Given:

`5y=7x-19`

Solve for `y` to get the equation into slope-intercept form:

`y=mx+b,`

where:

`m` is the slope, and `b` is the y-intercept.

`5y=7x-19`

Divide both sides by `5`.

`y=(7x)/5-19/5`

The y-intercept is the value of `y` when `x=0`.

The y-intercept is `(0,-19/5)` or `(0,-3.8)`

The x-intercept is the value of `x` when `y=0`.

Substitute `0` for `y` and solve for `x`.

`0=(7x)/5-19/5`

Multiply both sides by `5`.

`5xx0=7x-19`

Simplify.

`0=7x-19`

Add `19` to both sides.

`19=7x`

Divide both sides by `7`.

`19/7=x`

The x-intercept is `(19/7,0)~~(2.714,0)`

graph{y=7/5x-19/5 [-10, 10, -5, 5]}