How do you find the standard, point-slope, and slope intercept forms given m= -4/3, b=5/3?

1 Answer
Mar 24, 2018

Slope Intercept Form
y=-4/3x+5/3
Point-Slope Form
y-5/3=-4/3(x-0)
Standard Form
4x+3y=5

Explanation:

Slope Intercept Form
y=mx+b
y=-4/3x+5/3
Point-Slope Form
y-y_1=m(x-x_1)
We know that the y-intercept is (0,5/3), so we already know a point on the line.
y-5/3=-4/3(x-0)
Standard Form
ax+by=c
We can start off by using slope-intercept form, and then just solve for the constant (the integer).
y=-4/3x+5/3
4/3x+y=5/3 add 4/3 to both sides
4x+3y=5 Multiply the whole equation by 3 to achieve integer coefficients for every term (which is what standard form calls for)