Slope Intercept form is y = mx + b, where
m = the slope and b = the y- intercept.
Slope is determined by formula
#m = (y_2 - y_1)/(x_2-x_1)#
if you had the coordinates of two points on the line.
b is the point at which the line will cross (intercept) the y-axis.
If a problem asked for the slope intercept form and provides a slope and a single point on the line you could find the equation with two different methods.
What is the slope intercept equation of a line with a slope of m = 3/4 and a point on the line of (4 , 5)?
The first method is to us the slope-intercept equation and plug in values to solve for b.
5 = #3/4#(4) + b (simplify the fraction)
5 = 3 + b (isolate b)
5 - 3 = b (simplify)
b = 2
The slope-intecept equation would be y = #3/4#x + 2
The second method is to use the point-slope formula
#(y - y_1) = m(x - x_1)#
Plug in the information and simplify for the equation.
#(y - 5) = 3/4(x - 4)# (distribute the slope)
#(y - 5) = 3/4x - 3# (isolate y)
#y = 3/4x - 3 + 5# (simplify)
#y = 3/4x + 2# is the slope-intercept equation.