How do you write an equation in slope intercept form given the slope and a point?

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.

#(x_1,y_1) (x_2,y_2)#

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.