Write the equation of the line that passes through the points (3, -2) and (-2, 8) using the slope-intercept form.
My slope is -2
So if I substitute in one of the points, -2 = -2(3) + b
-2 = -6 + b
Add 6 to both sides and b = 4
So my equation is: y = -2x + 4
But.....the answer says y = -2x -1???
y = -2x-1 is clearly wrong, since neither of the given points satisfies that equation.
-2x+4 is in fact correct, as it's easy to check.
Thank you
To find the equation of the line that passes through two points using the slope-intercept form, you need to follow these steps:
1. Find the slope (m): The slope (m) can be found using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Let's calculate the slope using the points (3, -2) and (-2, 8):
m = (8 - (-2))/(-2 - 3) = 10/-5 = -2
2. Substitute the slope and one point into the slope-intercept form (y = mx + b): Now that we have the slope (m), we can choose one of the points and substitute its coordinates to solve for the y-intercept (b). Using the point (3, -2), we have:
-2 = -2(3) + b
-2 = -6 + b
b = -2 + 6
b = 4
3. Write the equation: Now that we have both the slope (m) and y-intercept (b), we can write the equation in slope-intercept form (y = mx + b):
y = -2x + 4
Based on the steps described, the equation you found, y = -2x + 4, is correct and matches the slope-intercept form for the line passing through the points (3, -2) and (-2, 8).
However, you mentioned that the given answer is y = -2x - 1. This may be a mistake in the answer key or a different set of calculations. It's essential to double-check the calculations and ensure that the correct coordinates of the given points were used in the calculations.