Question

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

Answer 1

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 = `(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 = `(y_2 - y_1) / (x_2 - x_1)`

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

m = `(0 - 3)/(4 - 2)`

m = `-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(x - x_1)`

We'll use the point (4, 0) for (`x_1, y_1`) but both points would give us the same end result.

y - 0 = `-3/2`(x - 4)

y = `-3/2x + 6`

Your equation is y = `-3/2x` + 6 with the slope being `-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 `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!