Question

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line? y = x – 12 y = x – 4 y = x + 2 y = x + 6

Answer 1

let line AB
2 - 4 ÷ 0 - 8
= 1 ÷ 4 is the aple of points (8,4) and (0,2)

Answer 2

GIVEN :

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y-4 = (x-8)

TO FIND :

The slope-intercept form of the equation for the given line.

SOLUTION :

From the given points (8, 4) and (0, 2) we can find the slope.

The formula for slope is

$m=\frac{y_2-y_1}{x_2-x_1}$ where m is slope

Let $(x_1,y_1)$  and  $(x_2,y_2)$ be the given points (8, 4) and (0, 2)  respectively

Substitute the points in the formula we get

$m=\frac{2-4}{0-8}$

$=-\frac{-2}{-8}$

$=\frac{1}{4}$

∴ $m=\frac{1}{4}$

The slope-intercept form is given by :

$y-y_1=m(x-x_1)$

Let $(x_1,y_1)$ be the point (8,4)

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

$4(y-4)=x-8$

$4y-16=x-8$

$4y=x-8+16$

$4y=x+8$

∴   the slope-intercept form of the equation for this line is $4y=x+8$

Option $4y=x+8$ is correct