A line passes through the points (-3,8) and (2,-2) write its equation in slope intercept form
To find the equation of a line in slope-intercept form, we need to find the slope and the y-intercept of the line.
First, let's find the slope of the line using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates of the given points: (-3,8) and (2,-2), we have:
y₁ = 8
y₂ = -2
x₁ = -3
x₂ = 2
Now we can plug these values into the formula to find the slope:
m = (-2 - 8) / (2 - (-3))
m = (-10) / (2 + 3)
m = (-10) / 5
m = -2
Now let's find the y-intercept. The y-intercept is the value of y when x is equal to 0. We can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Using the coordinates (-3,8), we have:
x = -3
y = 8
m = -2
Plugging these values into the equation y = mx + b:
8 = (-2)(-3) + b
8 = 6 + b
b = 8 - 6
b = 2
So, the y-intercept of the line is 2.
Now we can write the equation of the line in slope-intercept form using the slope (-2) and the y-intercept (2):
y = -2x + 2
Therefore, the equation of the line in slope-intercept form is y = -2x + 2.