Question

HELP I DON'T HAVE ENOUGH TIME!!!!

The equation y minus StartFraction 7 Over 2 EndFraction = one-half (x minus 4) is written in point-slope form. What is the y-intercept of the equation?
Negative StartFraction 11 Over 2 EndFraction
Negative one-half
One-half
Three-halves

Answer 1

The y-intercept of the equation is three-halves.

Step-by-step explanation:

Given,

$(y-\frac{7}{2})=\frac{1}{2}(x - 4)$

To find y-intercept. Plug x = 0,

$(y-\frac{7}{2}) = \frac{1}{2}(0-4)\\\\=> (y - \frac{7}{2}) = -2\\\\=> y = -2 + \frac{7}{2}\\\\=> y = \frac{-4 +7}{2}\\\\=> y = \frac{3}{2}$

Hence, the y-intercept of the equation is three-halves.

Answer 2

GIVEN :

Given equation is $y-\frac{7}{2}=\frac{1}{2}(x-4)$

TO FIND :

The y-intercept of the given equation.

SOLUTION :

From the given equation $y-\frac{7}{2}=\frac{1}{2}(x-4)$

$y-\frac{7}{2}=\frac{x}{2}-\frac{4}{2}$

$y-\frac{7}{2}=\frac{x}{2}-2$

$y=\frac{x}{2}-2+\frac{7}{2}$

$=\frac{x-4+7}{2}$

Adding the like terms

$=\frac{x+3}{2}$

$=\frac{x}{2}+\frac{3}{2}$

Split the fractions

∴ $y=\frac{x}{2}+\frac{3}{2}$

The general form of the y-intercept equation is:

y=mx+c

where  m is the slope and c is the y-intercept

Compare the above equation with the general form of the intercept form is y=mx+c we get

$c=\frac{3}{2}$

∴ the y- intercept for the given equation is $\frac{3}{2}$

∴ the option D) Three-halves is correct