Question

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

Answer 1

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.