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 of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (1, -3) and (3, 1), we can plug in the values into the formula:
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Now that we have the slope, we can use the slope-intercept form of a linear equation which is:
y = mx + b
We have the value of m, so let's plug it in:
y = 2x + b
To find the y-intercept (b), we can plug in the coordinates of one of the points into the equation and solve for b.
Using the point (1, -3), we have:
-3 = 2(1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Therefore, the equation of the line in slope-intercept form that passes through the points (1, -3) and (3, 1) is:
y = 2x - 5
To find the equation of a line in slope-intercept form, we need to determine the slope (m) and y-intercept (b).
Given the points (1, -3) and (3, 1), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates into the formula:
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Now that we have the slope, we can substitute it along with one of the points into the slope-intercept form equation (y = mx + b) to solve for the y-intercept (b).
Choosing the point (1, -3):
-3 = 2(1) + b
-3 = 2 + b
b = -5
Now that we have the slope (m = 2) and y-intercept (b = -5), we can write the equation in slope-intercept form:
y = 2x - 5
So, the correct equation in slope-intercept form for the line passing through the points (1, -3) and (3, 1) is y = 2x - 5.
To find the equation of a line in slope-intercept form, which is in the form of "y = mx + b" where "m" is the slope and "b" is the y-intercept, you need to follow these steps:
1. Calculate the slope (m) of the line using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's use the points (1, -3) and (3, 1) to find the slope:
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
2. Once you have the slope (m), you can substitute it into the slope-intercept form equation along with one of the points on the line to find the y-intercept (b). Let's use the point (1, -3):
-3 = 2(1) + b
-3 = 2 + b
b = -5
3. Now that you have the slope (m = 2) and the y-intercept (b = -5), you can form the equation:
y = 2x - 5
Therefore, the equation of the line that passes through the points (1, -3) and (3, 1) is y = 2x - 5.