Write a slope intercept equation for the line that passes through (2,-7) and (4,-13) Please show work,
To write a slope-intercept equation for the line passing through the points (2, -7) and (4, -13), follow these steps:
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Given points: (x1, y1) = (2, -7) and (x2, y2) = (4, -13)
m = (-13 - (-7)) / (4 - 2)
m = (-13 + 7) / 2
m = -6 / 2
m = -3
Step 2: Select one of the two points to use in the equation (x1, y1). Let's use (2, -7).
Step 3: Plug the values of the slope (m) and the coordinates (x1, y1) into the slope-intercept form, y = mx + b, to find the y-intercept (b).
-7 = -3(2) + b
-7 = -6 + b
b = -7 + 6
b = -1
Step 4: Write the slope-intercept equation using the values of the slope (m) and y-intercept (b).
y = -3x - 1
Therefore, the slope-intercept equation for the line passing through the points (2, -7) and (4, -13) is y = -3x - 1.