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

Oct 24, 2014

Slope Intercept form is y = mx + b, where
m = the slope and b = the y- intercept.

Slope is determined by formula

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

if you had the coordinates of two points on the line.

$\left({x}_{1} , {y}_{1}\right) \left({x}_{2} , {y}_{2}\right)$

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 = $\frac{3}{4}$(4) + b (simplify the fraction)

5 = 3 + b (isolate b)

5 - 3 = b (simplify)

b = 2

The slope-intecept equation would be y = $\frac{3}{4}$x + 2

The second method is to use the point-slope formula

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

Plug in the information and simplify for the equation.

$\left(y - 5\right) = \frac{3}{4} \left(x - 4\right)$ (distribute the slope)

$\left(y - 5\right) = \frac{3}{4} x - 3$ (isolate y)

$y = \frac{3}{4} x - 3 + 5$ (simplify)

$y = \frac{3}{4} x + 2$ is the slope-intercept equation.