Mathematics, 18.03.2021 01:50 keirarae2005

What is the equation of the line that passes through the points (-5,5) and has a slope of -1

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Answer from: estermartinez

Answer (assuming it can be in slope-intercept form):

y = -x

Step-by-step explanation:

1) Use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line in point-slope form. Substitute , x_1 , and y_1 for real values.

Since the represents the slope, substitute -1 in its place. Since x_1 and y_1 represent the x and y values of a point the line intersects, use the x and y values of the point (-5,5) for the formula. Substitute -5 for x_1 and 5 for y_1 .

$y-(5) = -1(x-(-5))\\y-5 = -1(x+5)$

2) From the above equation, isolate y to place the equation in slope-intercept form and find the final

$y-5=-1(x+5)\\y-5 = -x -5\\y = -x + 0\\y = -x$

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

step-by-step explanation:

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