How do you find the x and y intercepts for a line that goes through (2,1) and (6,4)?

Question

Isaiah Anthony · Accepted Answer

This appears to be a straight line. Determine the gradient before attempting to find the line's equation. #(4-1)/(6-2) = 3/4# Then substitute values into the equation #y-y1 = m(x-x1)#. I'm going to use (2,1). #y - 1 = 3/4(x-2)# #y-1=3/4x-1.5#
#y=3/4x-0.5# Now you know the y-intercept from the equation: #(0,-0.5)# Now, substitute #y=0# into the equation to find the x-intercept #0 = 3/4x-0.5#
#3/4x=0.5#
#x=2/3# The x-intercept is #(2/3,0)#

Ethan Adkins · Answer

undefined To find the x-intercept, set y = 0 in the equation of the line and solve for x. To find the y-intercept, set x = 0 in the equation of the line and solve for y. The equation of the line passing through (2,1) and (6,4) can be found using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. First, find the slope using the formula: m = (y2 - y1) / (x2 - x1). Then, use one of the given points to solve for b. Once you have the equation of the line, substitute 0 for x to find the y-intercept, and substitute 0 for y to find the x-intercept.