Final answer:
To find the equation of a line passing through two given points, use the slope-intercept form. The equation for the line passing through (-5, -4) and (3, -2) is y = (-1/4)x - 6.
Step-by-step explanation:
To find the equation of a line passing through two given points, we can use the slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept. First, we need to find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given coordinates, we have:
m = (-2 - (-4)) / (3 - (-5))
m = -2 / 8
So, the slope is -1/4. Now, we can choose any of the two points and substitute them into the slope-intercept form to find the y-intercept (b). Let's use the first point (-5, -4):
-4 = (-1/4)(-5) + b
Simplifying the equation, we get:
-4 = 5/4 + b
By rearranging the equation, we find that the y-intercept is -24/4 = -6. Therefore, the equation of the line is:
y = (-1/4)x - 6
Learn more about Equation of a line in slope-intercept form