How do you graph the line with slope -1/2 passing through point (-3,-5)?

1 Answer
Apr 25, 2017

Answer:

See explanation

Explanation:

#color(brown)("The slope (gradient) is stated as a single value so this is a straight line graph")#

#color(blue)("Determine the equation of the line")#

Gradient is #m=("change in y")/("change in x reading left to right")#

#m=("change in y")/("change in x reading left to right") = (-1)/2#

So the y value becomes less as you read left to right. The slope is down.

Let the given point be #P_1->(x_1,y_1)=(-3,-5)#

Using the standardised equation format #y=mx+c#

We have by substituting the values for #P_1#

#y_1=mx_1+c" "->" "-5=(-1/2)(-3)+c#

#" "-5=+3/2+c#

Subtract #3/2# from both sides to get #c# on its own.

#" "-5-3/2=0+c#

#" "-13/2=c#

So the equation of the line that passes through the point (-3,-5) is:
#y=-1/2x - 13/2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of the y-intercept")#

The y-intercept is the value of the constant #c=-13/2#

ie: set #x=0#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the value of the x-intercept")#

Set #y=0#

#y=-1/2x-13/2" "->" "0=-1/2x-13/2#

#1/2x=-13/2#

#x=-26/2 = -13#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mark your points on the x and y axis and draw a straight line through them. Also show the given point.
Tony B