Question

For the equation 3x-5y=10, state the slope, x-intercept, and y-intercept. Then find a slope that is perpendicular to the equation.

Answer 1

What does x-intercept and y-intercept mean?

X-intercept is when the line crosses the x-axis, which means y = 0.

Likewise, y-intercept is when the line crosses the y-axis, which means x = 0.

Substitute those values into the equation and solve for x and then solve for y.

Solve for x: 3x - 5(0) = 10

Solve for y: 3(0) - 5y = 10

In order to find your slope, you need to get your equation in this form:

y = mx + b

Through some basic algebra, you'll get
`y = (3)/(5) x - 2`

The number in the m position is your slope; m =
`(3)/(5)`

The slope of a perpendicular line is opposite and reciprocal,

so
`(3)/(5)` becomes
`-(5)/(3)`. Therefore, the perpendicular line is represented by the equation

`y = -(5)/(3)x + b`

Once you are given a point that this perpendicular line runs through, then you can substitute the (x, y) values into this equation and find
`b` (y-intercept).

Explanation: