The equation y-2/3=-2(x-1/4) is written in point-slope form. What is the equation in slope-intercept form?

Slope intercept form is given by
y=mx+b

So we want to get the y isolated on the left side.
First distribute the right side
Then add 2/3 to both sides of the equation to get y by itselft.

y-2/3=-2(x-1/4)
y-2/3=-2x+1/2
y=-2x+(3/6+4/6)
y=-2x+10/6
y=-2x+5/3

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-07-15T18:13:57+02:00

Answer: [tex] y=-2x+\dfrac{7}{6}[/tex]

Step-by-step explanation:

The slope -intercept form of a line is given by :-

[tex]y=mx+c[/tex]

The given equation of a line :[tex]y-\dfrac{2}{3}=-2(x-\dfrac{1}{4})[/tex]

To convert it into slope-intercept form , we need to multiply -2 inside the brackets , we get

[tex]y-\dfrac{2}{3}=-2x-\dfrac{-2}{4})\\\\\Rightarrow y-\dfrac{2}{3}=-2x+\dfrac{1}{2}\\\\\Rightarrow y=-2x+\dfrac{1}{2}+\dfrac{2}{3}\\\\\Rightarrow\ y=-2x+\dfrac{7}{6}[/tex]

Hence, the equation in slope-intercept form : [tex] y=-2x+\dfrac{7}{6}[/tex]