Question

Graph the line passing through (−4,−1) whose slope is m=-4/5

Answer 1

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

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The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

Answer 2

`y=-(4)/(5)x-(21)/(5)`

Explanation:

The fastest way is to use point-slope form with
`m=-(4)/(5)` and
`(x_1,y_1)=(-4,-1)`:

`y-y_1=m(x-x_1)\\y-(-1)=-(4)/(5)(x-(-4))\\y+1=-(4)/(5)(x+4)\\y+1=-(4)/(5)x-(16)/(5)\\y=-(4)/(5)x-(21)/(5)`