write slope intercept equation for the line that pass through (2,-7) and (4,-13)
y = m x + b
-7 = m(2) + b
-13 = m(4) + b
-----------------
6 = -2m
m = -3
-7 = -6 + b
b = -1
y = -3 x - 1
slope=(-13--7)/4-2 =-3
-7=-3*2+b
y intercept=-1
y=-3x-1
To find the slope-intercept equation for a line passing through two points, we can use the slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Given:
Point 1: (x1, y1) = (2, -7)
Point 2: (x2, y2) = (4, -13)
Using the formula, we can calculate the slope:
m = (-13 - (-7)) / (4 - 2)
m = (-13 + 7) / (4 - 2)
m = -6 / 2
m = -3
Step 2: Use the slope (m) and one of the points to find the y-intercept (b).
Using point 1: (x1, y1) = (2, -7)
y = mx + b
-7 = (-3)(2) + b
-7 = -6 + b
To isolate b, we can add 6 to both sides:
-7 + 6 = -6 + 6 + b
-1 = b
Step 3: Write the slope-intercept equation using the slope (m) and y-intercept (b):
y = mx + b
y = -3x + (-1)
The slope-intercept equation for the line that passes through (2, -7) and (4, -13) is y = -3x - 1.