Question

can you please help solve problem correctly. My daughter did problem completing wrong. Thanks

Answer 1

Recall that to compute the equation of a line we have to have two points on the line, once we have two points we can use the following formula for the equation (unless it is a vertical line):

$y-y_1=\frac{y_1-y_2}{x_1-x_2}(x-x_1),$

where (x₁,y₁) and (x₂,y₂) are two points on the line.

Now, notice that points (0,-1) and (3,2) are on line n, therefore its equation is:

$y-2=\frac{2-(-1)}{3-0}(x-3)\text{.}$

Simplifying the above equation we get:

$y-2=(x-3)\text{.}$

Two points on line m are: (0,4) and (1,2), therefore, its equation is:

$y-4=\frac{4-2}{0-1}(x-0)\text{.}$

Simplifying the above equation we get:

$y-4=-2x\text{.}$

Since line l is horizontal all its points will have the same y entry y=5, therefore, its equation is:

$y=4.$

Now, finally, when we have a vertical line its equation will be of the form x=k, where k is the x-entry of the points on the line. Notice that line p is a vertical line, and one point on the line is (-4,0), therefore its equation is:

$x=-4.$

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