What is an equation in slope-intercept form for the line that passes through points (1,-3) and (3,1)
slope = (1- -3) / (3-1) = 4/2
so
y = 2 x + b
now put in 1 for x and -3 for y to get b
To find the equation of the line that passes through the points (1,-3) and (3,1) in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the coordinates (1,-3) and (3,1):
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Step 2: Find the y-intercept (b)
The y-intercept (b) is the value of y when x = 0. We can use either point to find b.
Using the point (1,-3):
y = mx + b
-3 = 2(1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Step 3: Write the equation in slope-intercept form
Now that we have the slope (m = 2) and the y-intercept (b = -5), we can write the equation in slope-intercept form.
y = mx + b
y = 2x - 5
Therefore, the 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 written as y = mx + b, you need to determine the values of the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
The slope (m) is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (1, -3) and (3, 1):
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
So, the slope (m) of the line passing through the given points is 2.
Step 2: Find the y-intercept (b)
To find the y-intercept (b), substitute one of the given points into the equation and solve for b.
Using the point (1, -3), substitute the x and y values into the slope-intercept form equation, y = mx + b:
-3 = 2(1) + b
-3 = 2 + b
b = -5
So, the y-intercept (b) of the line passing through the given points is -5.
Step 3: Write the equation
Now that you have the values of the slope (m) and the y-intercept (b), you can write the equation in slope-intercept form:
y = mx + b
y = 2x - 5
Therefore, the equation in slope-intercept form for the line passing through the points (1, -3) and (3, 1) is y = 2x - 5.