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

Answer:

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:

$m = -\frac{1}{2}$

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

Substitute these given values in [1] we have;

$y-(-9) = -\frac{1}{2}(x-10)$

or

$y+9 = -\frac{1}{2}(x-10)$

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

$y+9 = -\frac{1}{2}x + 5$

Subtract 9 from both sides we get;

$y = -\frac{1}{2}x -4$

Therefore, the equation in slope intercept form(i.e y=mx+b) is, $y = -\frac{1}{2}x -4$

Answer 2

Answer:

y=-1/2x-4

Step-by-step 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.