Question

A line passes through the point (10, -9) and has a slope of - 1/2. Write an equation in slope intercept form for this line.

Answer 1

y=-1/2x-4

Explanation:

y=mx+c is slope-intercept form of line

where m denotes slope and c denotes y-intercept.

from question statement,we observe that

m=-1/2

slope intercept form becomes

y=-1/2x+c eq(1)

we have to find y-intercept.

To find y-intercept ,a point (10,-9) is given it means when x=10 ,y=-9

Put in eq(1)

-9=-1/2(10)+c

-9=-5+c

Adding 5 to both sides of above equation,we get

5-9=5-5+c

-4=c which is y-intercept.

put in eq(1),we get

y=-1/2x-4 is slope intercept form of line where slope is -1/2 and y-intercept is -4.

Answer 2

Point Slope intercept form:

The equation of the straight line is given by;

`y-y_1=m(x-x_1)` ......[1]

where

m represents the slope of a line.

As per the given statement:

`m = -(1)/(2)`

`(x_1, y_1) = (10, -9)`

Substitute these given values in [1] we have;

`y-(-9) = -(1)/(2)(x-10)`

or

`y+9 = -(1)/(2)(x-10)`

Using distributive property;
`a\cdot (b+c) = a\cdot b+ a\cdot c`

`y+9 = -(1)/(2)x + 5`

Subtract 9 from both sides we get;

`y = -(1)/(2)x -4`

Therefore, the equation in slope intercept form(i.e y=mx+b) is,
`y = -(1)/(2)x -4`