The equation of a line in the slope intercept form is expressec as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of the first and second points respectively
x1 and x2 are the x coordinates of the first and second points respectively
From the given points,
x1 = - 2, y1 = 7
x2 = 2, y2 = 4
By substituting these values into the formula,
m = (4 - 7)/(2 - - 2) = - 3/(2 + 2) = - 3/4
Slope = - 3/4
To find the y intercept, we would substitite m = - 3/4, x = - 2 and y = 7 into the slope intercept equation. We have
7 = - 3/4 * - 2 + c
7 = 3/2 + c
c = 7 - 3/2
c = 11/2
By substituting m = - 3/4 and c = 11/2, the equation of the line in slope intercept form is
y = - 3x/4 + 11/2