Write the equation of the line passing through the points (-1,2) and (3,4). A. Y=2x-2 b. Y= 2x-10 c. Y= 1/2x+5/2. D. Y=1/2x-5/2
To find the equation of the line passing through the points (-1,2) and (3,4), we first need to find the slope of the line.
The formula for finding the slope (m) between two points (x₁,y₁) and (x₂,y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (-1,2) and (3,4):
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Now that we have the slope, we can substitute it into the point-slope form of a linear equation, y - y₁ = m(x - x₁), where (x₁, y₁) is any point on the line (in this case, (-1,2)).
y - 2 = 1/2(x - (-1))
y - 2 = 1/2(x + 1)
y - 2 = 1/2x + 1/2
y = 1/2x + 1/2 + 2
y = 1/2x + 1/2 + 4/2
y = 1/2x + 5/2
Therefore, the equation of the line passing through the points (-1,2) and (3,4) is y = 1/2x + 5/2.
To find the equation of the line passing through the points (-1,2) and (3,4), we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
Here, m represents the slope of the line, and b represents the y-intercept.
Step 1: Calculate the slope (m)
The formula to find the slope between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
In this case, the coordinates are (-1,2) and (3,4):
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Step 2: Plug in the value of m and one of the points (x, y) into the slope-intercept form (y = mx + b).
Let's use the point (-1,2):
2 = (1/2)(-1) + b
2 = -1/2 + b
Step 3: Solve for the y-intercept (b).
By adding 1/2 to both sides of the equation:
2 + 1/2 = -1/2 + b + 1/2
5/2 = b
Step 4: Write the equation.
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line:
y = (1/2)x + 5/2
Therefore, the correct answer is D. Y = (1/2)x - 5/2.
To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m represents the slope of the line, and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1)/(x2 - x1)
Let's apply this formula using the given points (-1,2) and (3,4):
m = (4 - 2)/(3 - (-1))
= 2/4
= 1/2
Now that we have the slope (m = 1/2), we can substitute it into the slope-intercept form along with one of the points to find the y-intercept (b). Let's use the first point (-1,2):
y = mx + b
2 = (1/2)(-1) + b
2 = -1/2 + b
Now, let's solve for b:
2 + 1/2 = b
4/2 + 1/2 = b
5/2 = b
Therefore, the y-intercept is b = 5/2.
Now, we can substitute the values of m and b into the slope-intercept form to get the equation of the line:
y = 1/2x + 5/2
So, the correct answer is option D: Y = 1/2x - 5/2.