What is an equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1)?
a.) y= 3x + 1
b.) y= x - 3
c.) y= 2x + 5
d.) y= 2x - 5
(1, -3), (3, 1).
m = (1-(-3)/(3-1) = 4/2 = 2.
Y = mx + b.
-3 = 2*1 + b,
b = -5.
Y = 2x - 5.
To find the equation of a line in slope-intercept form, which is in the form y = mx + b, where m represents the slope and b represents the y-intercept, we can follow these steps:
1. Find the slope of the line using the formula:
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Given the points (1, -3) and (3, 1), let's substitute the coordinates into the slope formula:
slope (m) = (1 - (-3)) / (3 - 1)
slope (m) = 4 / 2
slope (m) = 2
2. Once we have determined the slope, we can use the point-slope form of a line, which looks like this:
y - y₁ = m(x - x₁)
Considering one of the given points, let's use the first point (1, -3) to write the equation:
y - (-3) = 2(x - 1)
y + 3 = 2(x - 1)
y + 3 = 2x - 2
3. Simplify the equation by isolating y on one side:
Subtract 3 from both sides of the equation:
y = 2x - 2 - 3
y = 2x - 5
Hence, the equation of the line in slope-intercept form that passes through the points (1, -3) and (3, 1) is y = 2x - 5. Therefore, option d) y = 2x - 5 is the correct answer.