Write the equation of the line with x-intercept 3 and passing through the point (5, 4) ? A) y − 2 = 1 2 (x − 4) B) y + 2 = 2(x + 4) C) y − 2 = 2(x − 4) D) y − 2 = 1 2 (x − 4)

I Don't understand the question, please help.

2 Answers
Feb 18, 2018

The line is #y=2x-6#.

Explanation:

We can find out the equation of the line by using the slope formula because we already know two points on the line: #(3,0)# (the #x#-intercept) and #(5,4)#.

#color(white)=>m=(y_2-y_1)/(x_2-x_1)#

#=>m=(4-0)/(5-3)#

#color(white)=>m=4/2#

#color(white)=>m=2#

Now, using point-slope form, we can use the slope and the points that we know to create an equation for the line.

#color(white)=>y-y_1=m(x-x_1)#

#=>y-4=2(x-5)#

You could leave it like this, or you could convert it to slope-intercept form by expanding a little further:

#y-4=2(x-5)#

#y-4=2x-10#

#y=2x-6#

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Feb 18, 2018

Neither of them

Explanation:

#y=2x-6# is the equation you're looking for; however, it is not found in any of the answers, assuming the x-intercept is #x=3#.
We can rewrite the equation, though, to best fit the answers (to compare).
Get rid of the -6 on the right side:
#y+6=2x-6+6#
#y+6=2x#
As you can see, the correct answer is not shown.