A line passes through the points (-3,-4) and (6,-10) write its equation in slope intercept form
To find the equation of a line in slope-intercept form (y = mx + b), you need to find the slope (m) and the y-intercept (b) of the line.
Step 1: Find the slope (m).
The formula for slope is (m = (y2 - y1) / (x2 - x1)), where (x1, y1) and (x2, y2) are the coordinates of the given points.
Using the points (-3,-4) and (6,-10):
m = (-10 - (-4)) / (6 - (-3))
m = (-10 + 4) / (6 + 3)
m = -6 / 9
m = -2/3
Step 2: Find the y-intercept (b).
We can choose either one of the given points to substitute into the equation.
Using the point (-3, -4):
y = mx + b
-4 = (-2/3)(-3) + b
-4 = 2 + b
b = -4 - 2
b = -6
Step 3: Write the equation in slope-intercept form.
Now that we have the slope (m = -2/3) and the y-intercept (b = -6), the equation of the line in slope-intercept form is:
y = (-2/3)x - 6