Answer:
To find the equation of a line passing through two points, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Find the slope (m)
The formula for slope (m) is (change in y) / (change in x). So, we can calculate it using the coordinates of the given points:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (-1, 10) and (4, -10), we get:
m = (-10 - 10) / (4 - (-1))
m = (-20) / (4 + 1)
m = (-20) / (5)
m = -4
Step 2: Find the y-intercept (b)
We can substitute the values of one of the points and the slope into the equation y = mx + b and solve for b.
Using the point (-1, 10), we have:
10 = (-4)(-1) + b
10 = 4 + b
b = 10 - 4
b = 6
Step 3: Write the equation in slope-intercept form
Now that we have the values of m and b, we can write the equation in slope-intercept form:
y = -4x + 6
So, the equation of the line passing through the points (-1, 10) and (4, -10) is y = -4x + 6 in slope-intercept form.
