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
First, we need to find the slope (m) of the line passing through the two given points.
The formula for slope is: m = (y2 - y1) / (x2 - x1)
Let's use the points (-1, 2) and (3, 4) to find the slope:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Now that we have the slope, we can use the point-slope form of a line to write the equation.
The point-slope form is: y - y1 = m(x - x1)
Using the point (-1, 2), we can write the equation of the line:
y - 2 = (1/2)(x - (-1))
y - 2 = (1/2)(x + 1)
y - 2 = (1/2)x + 1/2
Now, let's simplify the equation to the slope-intercept form (y = mx + b):
y = (1/2)x + 1/2 + 2
y = (1/2)x + 1/2 + 4/2
y = (1/2)x + 5/2
Therefore, the equation of the line passing through the points (-1, 2) and (3, 4) is y = (1/2)x + 5/2, which is option D.
To find the equation of the line passing through the points (-1, 2) and (3, 4), we will use the point-slope formula.
The point-slope formula is given by:
y - y1 = m(x - x1)
where (x1, y1) represents one point on the line, and m represents the slope of the line.
First, we need to find the slope (m) using the two points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates of the points into the slope formula:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Now that we have the slope, we can choose one of the points, (-1, 2), and place its coordinates into the point-slope formula:
y - 2 = (1/2)(x - (-1))
Simplifying further:
y - 2 = 1/2(x + 1)
Multiplying each term by 2 to eliminate the fractional coefficient:
2y - 4 = x + 1
Rearranging the equation to the standard form:
x - 2y = -5
Therefore, the equation of the line passing through (-1, 2) and (3, 4) is D. y = 1/2x - 5/2.
To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation, which is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) are the coordinates of the first point, and m is the slope of the line.
First, we need to find the slope, which can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given the points (-1, 2) and (3, 4), we can substitute the values into the equation to find the slope:
m = (4 - 2) / (3 - (-1))
= 2 / 4
= 1/2
Now that we have the slope (m = 1/2), we can choose any of the points to substitute into the point-slope form.
Let's choose the first point (-1, 2):
y - 2 = (1/2)(x - (-1))
y - 2 = (1/2)(x + 1)
y - 2 = (1/2)x + 1/2
Now, we can simplify the equation:
y = (1/2)x + 1/2 + 2
y = (1/2)x + 1/2 + 4/2
y = (1/2)x + 5/2
The equation of the line passing through the points (-1, 2) and (3, 4) is y = (1/2)x + 5/2.
Therefore, the correct answer is option D: y = 1/2x - 5/2.