Question

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

Answer 1

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`
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`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`
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`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`
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Mark your points on the x and y axis and draw a straight line through them. Also show the given point.