Question

identify an equation in point-slope form for the line parallel to y=1/2x-7 that passes through (-3,-2)

Answer 1

y=1/2x-7 has slope = 1/2
parallel  has same slope = 1/2

point-slope form equation
y + 2 = 1/2(x +3)

answer
y + 2 = 1/2(x +3)

Answer 2

Answer:

$\text{Required equation is }y=\frac{1}{2}x-\frac{1}{2}$

Step-by-step explanation:

Given the equation

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

we have to identify an equation that is parallel to above and passes through (-3,-2).

The slope-intercept form is

$y=mx+c$

where m is slope and c is y-intercept.

$\text{The given equation is in slope intercept form with slope }\frac{1}{2}$

As the slope of parallel lines are equal therefore the equation is

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

Now, the above equation pass through the point (-3, -2) therefore must satisfy the above equation

⇒ $-2=\frac{1}{2}(-3)+c$

$c=\frac{-1}{2}$

$\text{Hence, required equation is }y=\frac{1}{2}x-\frac{1}{2}$