How do you write an equation in standard form for a line with y- intercept of 3/2 and slope of m = 1/2?

Question

Ethan Adkins · Accepted Answer

In slope-intercept form, a line with y-intercept of #3/2# and a slope of #m=1/2# would be written as
#color(white)("XXXXX")##y=1/2x+3/2# Standard form is (normally)
#color(white)("XXXXX")##Ax+By=C# where #A>=0 and AepsilonZZ# Converting to standard form.
Multiply everything by 2 to clear the fractions
#color(white)("XXXXX")##2y=1x+3#
Subtract #2y+3# from both sides (and flip the sides)
#color(white)("XXXXX")##1x-2y = -3#
#color(white)("XXXXX")##color(white)("XXXXX")#which is in standard form

Eva Abramson · Answer

undefined The equation of a line in standard form is $ Ax + By = C $, where A, B, and C are integers, and A is positive. To write the equation of a line with a y-intercept of $ \frac{3}{2} $ and a slope of $ m = \frac{1}{2} $ in standard form, we follow these steps:

1. Start with the slope-intercept form of the equation: $ y = mx + b $, where m is the slope and b is the y-intercept.
2. Substitute the given values into the equation: $ y = \frac{1}{2}x + \frac{3}{2} $.
3. Multiply both sides of the equation by 2 to clear the fraction: $ 2y = x + 3 $.
4. Move the x term to the left side of the equation: $ -x + 2y = 3 $.
5. Multiply through by -1 to make the coefficient of x positive: $ x - 2y = -3 $.

Therefore, the equation of the line in standard form is $ x - 2y = -3 $.

Isaiah Anthony · Answer

undefined To write an equation in standard form for a line with a y-intercept of $ \frac{3}{2} $ and a slope of $ m = \frac{1}{2} $, you can use the slope-intercept form of a linear equation, which is $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

Substituting the given values, the equation becomes $ y = \frac{1}{2}x + \frac{3}{2} $.

To convert this equation into standard form, move all terms to one side so that the equation is in the form $ Ax + By = C $, where $ A $, $ B $, and $ C $ are integers and $ A $ is positive:

$$ 2y = x + 3 $$

$$ -x + 2y = 3 $$

$$ -x + 2y - 3 = 0 $$

Thus, the equation in standard form for the given line is $ -x + 2y - 3 = 0 $.