What equation represents the line that passes through the points (6,-3)and (-4,-9)?
(Y1-Y2)/(X1-X2) = (y+3)/(x-6)
(-3 +9)/(6+4) = (y+3)/(x-6)
6/10 = 3/5 = (y+3)/(x-6)
5(y+3) = 3(x-6)
your turn
I think the answer would be y - 3 = 3/5 (X+6)
the answer was D
To find the equation of a line that passes through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Given points:
(6, -3): (x1, y1)
(-4, -9): (x2, y2)
Substituting the values into the formula:
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
Using one of the given points (6, -3), we can substitute the coordinates to find b:
-3 = (3/5)(6) + b
-3 = 18/5 + b
To isolate b, subtract 18/5 from both sides:
-3 - 18/5 = b
(-15/5) - (18/5) = b
-33/5 = b
Therefore, the y-intercept (b) is -33/5.
Now, we can write the equation of the line:
y = (3/5)x - 33/5.