Question

How do you find slope and intercepts to graph `9x-5y=4`?

Answer 1

`m=9/5`; with points `(0,-4/5)` and `(1,1)`

Explanation:

Convert the equation into slope-intercept form by solving for `y`.

`-5y=-9x+4` => subtracting both sides by -9x

`y=9/5x-4/5` = > dividing by -5

The slope-intercept equation takes the form of `y=mx+b`. The slope `m` would be the coefficient of x, and the constant `b`, the y-intercept (value of `y` if `x=0`), thus yielding: `m=9/5` and `b=-4/5`.

This gives us one point on the line: `(0,-4/5)`.

To get another point on the line, substitute any number for x and solve for y. For ease in graphing, choose an integer close to the first point. For this example, let `x=1`.

`y=9/5*(1)-4/5` => by substitution
`y=9/5-4/5=5/5or 1`

Thus, point `(1,1)` also belongs to the line. From here, the two points can be connected, and a line can be formed accordingly.

graph{9x-5y=4 [-2.657, 2.657, -1.328, 1.328]}

Source: https://www.mathplanet.com/education/algebra-1/formulating-linear-equations/writing-linear-equations-using-the-slope-intercept-form