Question

Find an equation for the line with the given properties. Express the equation in slope-intercept form. Containing the points (-3, 5) and (2, -1).

a) y = -2x + 1
b) y = 2x + 1
c) y = -2x - 1
d) y = 2x - 1

Answer 1

To find the equation of a line using two points, calculate the slope using the formula (y2 - y1) / (x2 - x1), and then substitute the coordinates of one of the points to find the y-intercept. The correct equation for the line passing through (-3, 5) and (2, -1) is y = (-6/5)x + 1.

Step-by-step explanation:

To find the equation of a line using two points, we first need to determine the slope of the line. The slope, denoted as 'm', can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the given points (-3, 5) and (2, -1), we can calculate the slope as follows:

m = (-1 - 5) / (2 - (-3)) = -6 / 5

Now that we have the slope, 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. To find the y-intercept, we can substitute the coordinates of one of the points into the equation:

5 = (-6/5)(-3) + b

After simplifying, we find b = 1. Thus, the equation of the line is y = (-6/5)x + 1. Comparing this with the given options, the correct answer is y = (-6/5)x + 1.