Question

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = y minus 4 equals StartFraction one-fourth EndFraction left-parenthesis x minus 9 right-parenthesis.(x – 8). What is the slope-intercept form of the equation for this line?

a. y = y equals StartFraction one-fourth EndFraction x minus 12.x – 12
b. y = y equals StartFraction one-fourth EndFraction x minus 4.x – 4
c. y = y equals StartFraction one-fourth EndFraction x plus 2.x + 2
d. y = y equals StartFraction one-fourth EndFraction x plus 6.x + 6

Answer 1

Correct question: The correct form of the exercise is: "The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = (x - 8)/4 . What is the slope-intercept form of the equation for this line?

Answer:  c)y = x/4 +2

Concept: Equation of line in slope intercept form is given by

y = mx +c

m = slope of line

c = y intercept of line

Given: Equation of line

y - 4 = (x - 8)/4

To find: Equation of line in slope intercept form.

Step-by-step explanation:

Given the equation of the line in Point-Slope form

y - 4 = (x - 8)/4

Equation of line in slope intercept form is given by

y = mx +c

m = slope of line

c = y intercept of line

solve for "y" in order to write the given equation of the line in Slope

Intercept form.

y - 4 = (x - 8)/4

y - 4 = x/4  - 8/4

y - 4  = x/4  -  2

y = x/4  - 2  + 4

y = x/4  + 2

Equation of line in slope intercept form

y = x/4  + 2

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Answer 2

Answer:

The answer is option (C). $y=\frac{1}{4} x+2$

$y=y$ equals Start Fraction one-fourth End Fraction x plus $2.x+2$

step-by-step explanation:

The equation of a line passing between the points (8, 4) and (0, 2) is expressed in the point-slope form is $y-4=\frac{1}{4} (x-8)$

What does this line's equation look like in slope-intercept form?

Slope-Intercept form of the line's equation is

$y = mx+b$

where "m" is the slope and "b" is the y-intercept

Using the line's equation in point-slope form

$y-4=\frac{1}{4} (x-8)$

To construct the following equation of the line in Slope Intercept form, you must get the value of "y"

Then,

$y-4=\frac{1}{4} (x-8)$

$y-4=\frac{1}{4} x-\frac{8}{4}$

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

$y=\frac{1}{4} x-2+4$

$y=\frac{1}{4} x+2$

Identify the slope "m" for what it is

$m=\frac{1}{4}$

The y-intercept "b" is also

$b = 2$

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