Which equation in slope-intercept form represents a line that is parallel to y=1/2x−2 and passes through the point (−8,1)?
y=−1/2x+5
y=1/2x+5
y=1/2x−9
y=−2x−7
y=−2x−5
....Btw the answer is y=1/2x+5...
Just for yall in the future ;)
Well, I must say that equations can be quite parallel-izing! In this case, we want a line parallel to y = (1/2)x - 2, which means it must have the same slope. Coincidentally, the slope-intercept form of an equation is y = mx + b, where m represents the slope. So, we're looking for an equation with a slope of 1/2.
Looking at the given options, the only equation that fits the bill is y = (1/2)x + 5. It's parallel to the original line, and it passes through the point (-8, 1). That equation definitely didn't take any detours!
To find the equation of a line parallel to y=1/2x−2 and passing through the point (-8,1), we can use the same slope as the given line, which is 1/2.
We can use the point-slope form of a linear equation, which is y-y1=m(x-x1). Here, m represents the slope and (x1, y1) represents the given point.
Substituting the values, we have:
y-1 = 1/2(x-(-8))
Simplifying, we get:
y-1 = 1/2(x+8)
Expanding the parentheses, we have:
y-1 = 1/2x + 4
Now, let's isolate y:
y = 1/2x + 4 + 1
Simplifying further:
y = 1/2x + 5
Therefore, the equation in slope-intercept form that represents a line parallel to y=1/2x−2 and passing through the point (-8,1) is:
y = 1/2x + 5
So, the correct option is: y=1/2x+5.
To find the equation of a line that is parallel to the given line and passes through the point (-8,1), we need to use the fact that parallel lines have the same slope.
The given equation is y = (1/2)x - 2, which is in slope-intercept form (y = mx + b) where m is the slope.
The slope of the given line is 1/2, so any line that is parallel to it will also have a slope of 1/2.
Now, we can use the point-slope form of a linear equation to find the equation of the line that passes through (-8,1) with a slope of 1/2.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Substituting the values into the equation, we get: y - 1 = (1/2)(x - (-8))
Simplifying, we have: y - 1 = (1/2)(x + 8)
Expanding the equation, we get: y - 1 = (1/2)x + 4
Now, isolate y to rewrite the equation in slope-intercept form:
y = (1/2)x + 4 + 1
Simplifying further, we have: y = (1/2)x + 5
Therefore, the equation that represents a line parallel to y = (1/2)x - 2 and passes through the point (-8,1) is y = (1/2)x + 5.
So, the correct answer is y = (1/2)x + 5.
slope is 1/2
so,
y = 1/2 x + b
So, find b such that
1 = 1/2 * -8 + b