which equation represents the line that passes through the points (6, -3) and (-4, -9)
y+4 = 3/5(x + 9)
y+4 = 5/3(x + 9)
y+3 = 3/5(x + 6)
y+3 = 3/5(x - 6)
well, the slope is 3/5, so what do you think?
To find the equation of a line passing through two given points, you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
To determine the slope (m), you can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let's calculate the slope:
m = (-9 - (-3)) / (-4 - 6)
m = (-9 + 3) / (-4 - 6)
m = -6 / (-10)
m = 3/5
Now that we have the slope, we can substitute it into the slope-intercept form (y = mx + b) and solve for the y-intercept (b).
Using the point (6, -3):
-3 = (3/5)(6) + b
-3 = 18/5 + b
Multiply both sides by 5 to eliminate the fraction:
-15 = 18 + 5b
-15 - 18 = 5b
-33 = 5b
b = -33/5
Therefore, the equation of the line that passes through the points (6, -3) and (-4, -9) is:
y = (3/5)x - 33/5
Now let's check if any of the given options match the derived equation:
- y + 4 = (3/5)(x + 9)
- y - 3 = (3/5)(x - 6)
Comparing both options to the derived equation, we can see that the correct answer is:
y - 3 = (3/5)(x - 6)