Final answer:
To write the equation of a line passing through two points in slope-intercept form, we need to find the slope and the y-intercept. The slope is calculated using the formula (y2 - y1) / (x2 - x1), and the y-intercept is found by substituting one of the given points into the equation. The equation of the line passing through (-4, 9) and (4, -15) is y = -3x - 3.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept. The slope of a line passing through two points, (x1, y1) and (x2, y2), is calculated using the formula m = (y2 - y1) / (x2 - x1). Let's calculate the slope first:
m = (-15 - 9) / (4 - (-4)) = -24 / 8 = -3
Now, let's use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. We can substitute one of the given points into the equation to find the value of b:
9 = -3(-4) + b
9 = 12 + b
b = 9 - 12 = -3
So, the equation of the line passing through the points (-4, 9) and (4, -15) in slope-intercept form is y = -3x - 3.
Learn more about writing the equation of a line in slope-intercept form