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

Question

Kennedy Adams · Accepted Answer

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

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: 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!

Savannah Anderson · Answer

undefined To write the equation of a line passing through the point (2,3) with an x-intercept of 4, you can use the point-slope form of the equation:

$$ y - y_1 = m(x - x_1) $$

where $ (x_1, y_1) $ is the point (2,3), and $ m $ is the slope.

First, calculate the slope using the given points:

$$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

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

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

Now substitute the values into the point-slope form:

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

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

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

This is the equation of the line passing through the point (2,3) with an x-intercept of 4.