How do you write out the equation of the line passing through (1,5) (6,15)?

2 Answers
Nov 15, 2016

y=2x+3

Explanation:

Use point-slope and slope formula.

We first need to find the slope by finding the change in y over the change in x. This would be (15-5)/(6-1)=10/5, which gives us 2.

Now if we look at point slope formula, it is y-y_1=m(x-x_1) where x_1 and y_1 are the x and y coordinates of a given point. Let's just say we plug in (1,5) for it and the 2 for m which is slope.

y-5=2(x-1)

Add 5 to both sides.

y\cancel(-5)\cancel(\color(indianred)(+5))=2(x-1)\color(indianred)(+5)

Distribute 2

y=\color(navy)(2x-2)+5

Add -2 and 5

y=2x+\color(olive)(3)

Nov 15, 2016

y=2x+3

Explanation:

Apply slope formula

  • use formula m=(y_2-y_1)/(x_2-x_1) given two points (x_1,y_1) and (x_2,y_2) (doesn't matter which one comes first)
    the slope you get should be \color(olive)(m)=10/5=2/1=\color(olive)(2)

Apply point-slope formula

  • now plug-in one of the points for the formula y-y_1=m(x-x_1),
    which will now become y-y_1=\color(olive)(2)(x-x_1).
    here, \color(indianred){(x_1,y_1)} can be either of the points.
    for easier explanation, used \color(indianred){(1,5)}

Working it out

step A \color(maroon)(rightarrow)plugging in: y-\color(indianred)(5)=2(x-\color(indianred)(1))
step B \color(maroon)(rightarrow)distributing: y-5=\color(seagreen)(2x-2)
step C \color(maroon)(rightarrow)\color(teal)(5) added to each side: y\cancel(-5)\cancel(\color(teal){+5})=2x-2\color(teal)(+5)
step D \color(maroon)(rightarrow)simplifying like terms: y=2x+\color(green)(3)

  • therefore the equation is:
    \color{cornflowerblue}{y=2x+3}