How do you write the equation of a line in slope intercept, point slope and standard form given Point: (-5, 4) Slope: m = 2?

1 Answer
Jun 2, 2018

Slope intercept: y=2x+14
Point-slope: y=2x+14
Standard form: 2x-y=-14

Explanation:

Slope intercept equation is y=mx+c, where m is the slope/gradient, c is the y-intercept and (x, y) is the format of the points/coordinates given (-5, 4).

The point-slope is given as y-y_1=m(x-x_1).

The standard form of an equation is Ax+By=C.

Now, for slope intercept, substitute all the values you have been given and solve for c, the y-intercept:

y=mx+c
4=2(-5)+c
4=-10+c
c=14

Then substitute only m and c to get the equation of the slope-intercept:

y=2x+14

Now for the point-slope (which is just another method of finding the equation of the slope), you find that there's y_1 and x_1 in the formula, this corresponds to the x and y of the coordinates of the points you have been given, (-5, 4). Where (x_1, y_1).

So, substitute the values of y_1, x, and x_1 and isolate y to find the equation of the point-slope:

y-y_1=m(x-x_1)
y-(4)=2(x-(-5))
y-4=2(x+5)
y-4=2x+10
y=2x+10+4
y=2x+14

As you can see, both methods give the same results by substitution.

For the standard form, you use the format of the equation of the point-slope but rearrange it so that the x and y terms are on one side of the equal sign and the constants are on the other, Ax+By=C:

y-4=2(x+5)
y-4=2x+10
-2x+y=14

This is almost in the format of Ax+By=C but Ax cannot have a negative sign in front of it. To get rid of this negative, divide both sides of the equation by -1:

(-2x+y)/-1=14/-1
2x-y=-14

Which can also be solved by taking the results from one of the other equations and rearranged to follow the format of Ax+By=C.

Hope this helps.