A line passes through the point (10,-2) and has a slope of 1/2

Question

Write an equation in Ax+By=C form for this line.

Use integers for A,B and C.

Answer 1

To write in the standard form Ax+By+c=0

m=1/2

m=A/B

so A=1, B=2

we had y=1/2x-7

rewriting

y-1/2x+7=0

clearing out the fraction

2y-x+14,

-x+2y+14=0

A=-1, B=2, C=14

Answer 2

Hi Jocelyn M.

-(1/2)x + y = -7

For your line you are given a point (10,-2) and the slope m=1/2

Use this information to get started since you have a slope you can use the Slope Intercept Form

y=mx + b

y=(1/2)x + b

Use the coordinates of the point given to solve for b

-2 = (1/2)10 + b

-2 = 5 + b

Subtract 5 from both sides

-2 - 5 =b

-7 =b

Now we have the line in Slope Intercept Form

y = mx + b

y = (1/2)x -7

Just subtract (1/2)x from both side to get it into Ax + By = C

-(1/2)x + y = -7

You can check by plugging the x coordinate of the point (10, -2) to see if it yields the y coordinate

-(1/2)10 + y = -7

-5 + y = -7

Add 5 to both sides of the equation

y = -7 + 5

y = -2

I hope you find this useful.