# How do you write an equation of a line passing through (2,3) with x-intercept 4?

Jan 30, 2016

The x intercept is (4, 0), which is just another point on the line.

#### Explanation:

We can find the point slope form of the line but first we must find the slope of the line.

The formula for slope is m = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, where m represents slope, (${x}_{2} , {y}_{2}$) and (${x}_{1} , {y}_{1}$) represent separate points.

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

Let point 1 be (2, 3) and point 2 (4,0).

m = $\frac{0 - 3}{4 - 2}$

m = $- \frac{3}{2}$

Now that we know the slope we can use point slope form to find the equation of our line.

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

We'll use the point (4, 0) for (${x}_{1} , {y}_{1}$) but both points would give us the same end result.

y - 0 = $- \frac{3}{2}$(x - 4)

y = $- \frac{3}{2} x + 6$

Your equation is y = $- \frac{3}{2} x$ + 6 with the slope being $- \frac{3}{2}$ and the y intercept 6.

Practice Exercises:

1. Find the equations of the following lines:

a). Has a y intercept of -3 and a slope of $\frac{2}{5}$

b). Passes through (-3,6) and (-1,7)

c) Has an x intercept of 2 and a y intercept of -9.

Good luck!