Question

Write an equation of the line that passes through the given points (-1,3) and (4, -7). The equation is in slope-intercept form.

A. y = -2x + 1
B. y = -2x - 1
C. y = 2x + 1
D. y = 2x - 1

Answer 1

The equation of the line that passes through the points (-1,3) and (4, -7) is y = -2x + 1, which corresponds to option A.

Step-by-step explanation:

To write an equation of the line in slope-intercept form that passes through the points (-1,3) and (4, -7), we first need to find the slope (m) of the line. The slope can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given points into the formula, we get:

m = (-7 - 3) / (4 - (-1))

m = -10 / 5

m = -2

Now that we have the slope, we can use one of the points to find the y-intercept (b) with the formula:

y - y1 = m(x - x1)

Using the point (-1, 3), we obtain:

3 - (-2)(-1) = b

3 - 2 = b

b = 1

Therefore, the equation of the line is y = mx + b, which translates to:

y = -2x + 1

The correct answer is: A. y = -2x + 1.