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
First, we need to find the slope of the line. The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, the points are (1, -3) and (3, 1). Plugging these values into the formula, we get:
m = (1 - (-3)) / (3 - 1)
= (1 + 3) / (3 - 1)
= 4 / 2
= 2
Now that we have the slope (m = 2), we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept. We still need to find the y-intercept (b). To do this, we can use one of the given points. Let's use (1, -3):
-3 = 2(1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Now we have the slope (m = 2) and the y-intercept (b = -5), so the equation of the line in slope-intercept form is:
y = 2x - 5
Therefore, the correct response is y = 2x - 5.