What is an equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1)?
To find the equation of a line in slope-intercept form, we need to determine the slope of the line and the y-intercept.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Let's use the points (1, -3) and (3, 1) to find the slope:
m = (1 - (-3)) / (3 - 1)
= 4 / 2
= 2
Now we have the slope (m = 2), we just need to find the y-intercept (b).
We can use the point-slope form of a line:
y - y₁ = m(x - x₁)
Using the point (1, -3) and the slope (2):
y - (-3) = 2(x - 1)
y + 3 = 2(x - 1)
Now let's simplify the equation:
y + 3 = 2x - 2
To write the equation in slope-intercept form, isolate y:
y = 2x - 2 - 3
y = 2x - 5
Therefore, the equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1) is y = 2x - 5.