Convert the equation into slope-intercept form by solving for yy.
-5y=-9x+4 −5y=−9x+4 => subtracting both sides by -9x
y=9/5x-4/5y=95x−45 = > dividing by -5
The slope-intercept equation takes the form of y=mx+by=mx+b. The slope mm would be the coefficient of x, and the constant bb, the y-intercept (value of yy if x=0x=0), thus yielding: m=9/5m=95 and b=-4/5b=−45.
This gives us one point on the line: (0,-4/5)(0,−45).
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=1x=1.
y=9/5*(1)-4/5y=95⋅(1)−45 => by substitution
y=9/5-4/5=5/5or 1y=95−45=55or1
Thus, point (1,1)(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
