Answer :
To convert the given point-slope form equation [tex]\( y - \frac{2}{3} = -2 \left( x - \frac{1}{4} \right) \)[/tex] into slope-intercept form [tex]\( y = mx + b \)[/tex], follow these steps:
1. Distribute the slope on the right side:
[tex]\[ y - \frac{2}{3} = -2 \left( x - \frac{1}{4} \right) \][/tex]
Expand the right side by distributing [tex]\(-2\)[/tex]:
[tex]\[ y - \frac{2}{3} = -2x + 2 \cdot \frac{1}{4} \][/tex]
Since [tex]\( 2 \cdot \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \)[/tex], we get:
[tex]\[ y - \frac{2}{3} = -2x + \frac{1}{2} \][/tex]
2. Isolate [tex]\( y \)[/tex] by adding [tex]\(\frac{2}{3}\)[/tex] to both sides of the equation:
[tex]\[ y = -2x + \frac{1}{2} + \frac{2}{3} \][/tex]
3. Combine the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex] on the right side:
To combine these fractions, find a common denominator. The common denominator for 2 and 3 is 6. Convert each fraction:
[tex]\[ \frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6} \][/tex]
Adding these fractions:
[tex]\[ \frac{1}{2} + \frac{2}{3} = \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \][/tex]
4. Substitute back into the equation:
[tex]\[ y = -2x + \frac{7}{6} \][/tex]
Thus, the equation in slope-intercept form is:
[tex]\[ y = -2x + \frac{7}{6} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{y = -2x + \frac{7}{6}} \][/tex]
1. Distribute the slope on the right side:
[tex]\[ y - \frac{2}{3} = -2 \left( x - \frac{1}{4} \right) \][/tex]
Expand the right side by distributing [tex]\(-2\)[/tex]:
[tex]\[ y - \frac{2}{3} = -2x + 2 \cdot \frac{1}{4} \][/tex]
Since [tex]\( 2 \cdot \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \)[/tex], we get:
[tex]\[ y - \frac{2}{3} = -2x + \frac{1}{2} \][/tex]
2. Isolate [tex]\( y \)[/tex] by adding [tex]\(\frac{2}{3}\)[/tex] to both sides of the equation:
[tex]\[ y = -2x + \frac{1}{2} + \frac{2}{3} \][/tex]
3. Combine the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex] on the right side:
To combine these fractions, find a common denominator. The common denominator for 2 and 3 is 6. Convert each fraction:
[tex]\[ \frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6} \][/tex]
Adding these fractions:
[tex]\[ \frac{1}{2} + \frac{2}{3} = \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \][/tex]
4. Substitute back into the equation:
[tex]\[ y = -2x + \frac{7}{6} \][/tex]
Thus, the equation in slope-intercept form is:
[tex]\[ y = -2x + \frac{7}{6} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{y = -2x + \frac{7}{6}} \][/tex]
Answer:
B. y=-2x+7/6
Step-by-step explanation:
y - 2/3 = -2 ( x-1/4)
Slope intercept form is y = mx+b where m is the slope and b is the y intercept.
Distribute the 2.
y -2/3 = -2x + 1/2
Add 2/3 to each side.
y - 2/3 + 2/3 = -2x + 1/2 + 2/3
y = -2x+ 1/2 + 2/3
Get a common denominator of 6.
y = -2x + 3/6 + 4/6
y = -2x+ 7/6