What is an equation in slope-intercept form for the line that passes through the points (1, –3) and (3, 1)?
(1 point)
Responses
y = 3x + 1
y = 3 x + 1
y = x – 3
y = x – 3
y = 2x + 5
y = 2 x + 5
y = 2x – 5
To find the equation in slope-intercept form, we need to first find the slope (m) and then use one of the given points and the slope in the equation.
The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Given the points (1, -3) and (3, 1):
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
So the slope (m) is 2.
Now, we can use one of the points and the slope in the equation y = mx + b, where m is the slope and b is the y-intercept.
Using the point (1, -3):
-3 = 2(1) + b
-3 = 2 + b
b = -5
Now we have the slope (m = 2) and the y-intercept (b = -5), so we can write the equation in slope-intercept form:
y = 2x - 5
Therefore, the correct equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1) is y = 2x - 5.
To find the equation of the line in slope-intercept form, we can use the formula:
y = mx + b
First, let's determine the slope, which is denoted by "m." The slope is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (1, -3) and (3, 1):
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Now that we have the slope, we can substitute it into the equation along with one of the given points to solve for the y-intercept, denoted by "b." Let's use the point (1, -3):
-3 = 2(1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Now we have the slope (m = 2) and the y-intercept (b = -5). Plugging these values into the slope-intercept form equation, we get:
y = 2x - 5
So, the equation in slope-intercept form for the line passing through the points (1, -3) and (3, 1) is:
y = 2x - 5