write an equation in slope-intercept form for the line passing through (-2,6) and (4,-3)
To write the equation of the line passing through two points (-2,6) and (4,-3) in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Step 1: Find the slope (m).
The slope (m) is given by the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the coordinates (-2,6) and (4,-3), we have:
m = (-3 - 6) / (4 - (-2))
m = (-3 - 6) / (4 + 2)
m = -9 / 6
m = -3/2
Step 2: Find the y-intercept (b).
To find the y-intercept (b), we can substitute one of the given points' coordinates into the slope-intercept form equation.
Using the point (-2,6), we have:
6 = (-3/2)(-2) + b
6 = 3 + b
b = 6 - 3
b = 3
Step 3: Write the equation.
Now that we have found the slope (m = -3/2) and the y-intercept (b = 3), we can write the equation in slope-intercept form.
The equation is:
y = (-3/2)x + 3
slope = (-3-6)/(4+2) = -9/6 = -3/2
so y = (-3/2)x + b
sub in (-2,6) and solve for b
replace in the equation and you are done