What is an equation in slope-intercept form for the line that passes through the points (1, –3) and (3, 1)?
To write the equation of a line in slope-intercept form, which is y = mx + b, we need to find the slope (m) and the y-intercept (b) of the line.
First, let's calculate the slope (m) using the two given points (1, –3) and (3, 1). The slope is the change in y divided by the change in x, often written as:
m = (y2 - y1) / (x2 - x1)
Let's assign these coordinates as follows:
x1 = 1, y1 = -3
x2 = 3, y2 = 1
Now, apply these values to the slope formula:
m = (1 - (-3)) / (3 - 1)
m = (1 + 3) / (2)
m = 4 / 2
m = 2
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (1, –3). We substitute x with 1, y with -3, and m with 2 into the slope-intercept formula:
-3 = (2)(1) + b
Now, we solve for b:
-3 = 2 + b
b = -3 - 2
b = -5
Finally, the equation of the line in slope-intercept form is:
y = mx + b
y = 2x - 5
This is the line that passes through the points (1, –3) and (3, 1).