Question

The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = (x – 1). What is the slope-intercept form of the equation for this line?
y =1/2 x + 2
y = 1/2x – 4
y = 1/2x + 5/2
y = 1/2x – 7/2

Answer 1

(-9,-2) (1,3)
slope = (3 - (-2) / (1 - (-9) = 5/10 = 1/2

y - y1 = m(x - x1)
slope(m) = 1/2
(1,3)...x1 = 1 and y1 = 3
sub
y - 3 = 1/2(x - 1)
y - 3 = 1/2x - 1/2
y = 1/2x - 1/2 + 3
y = 1/2x - 1/2 + 6/2
y = 1/2x + 5/2 <=== slope intercept form

Answer 2

Answer: $y=\dfrac{1}{2}x+\dfrac{5}{2}$

Step-by-step explanation:

Equation of a line passing through points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Similarly, the equation of line passing through (-9, -2) and (1, 3) is given by :-

$(y-3)=\dfrac{3-(-2)}{1-(-9)}(x-1)$

$(y-3)=\dfrac{3+2}{1+9)}(x-1)$

$(y-3)=\dfrac{5}{10}(x-1)$

$(y-3)=\dfrac{1}{2}(x-1)$

$(y-3)=\dfrac{1}{2}x-\dfrac{1}{2}$

Add 3 both sides , we get

$y=\dfrac{1}{2}x-\dfrac{1}{2}+3$

$y=\dfrac{1}{2}x+\dfrac{(2)(3)-1}{2}$

$y=\dfrac{1}{2}x+\dfrac{5}{2}$

Hence, he slope-intercept form of the equation for this line :

$y=\dfrac{1}{2}x+\dfrac{5}{2}$