What is the equation of the line that passes through the point (-5, -4) and has a slope of – 3/5?

             y + 4 = -³/₅(x + 5)      {the point-slope form of the equation }

             y = -³/₅x - 7               {the slope-intercept form of the equation}

             3x + 5y = - 35               {standard form of the equation}

Step-by-step explanation:

The point-slope form of equation is : y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through.

m = -³/₅

(-5, -4)    ⇒   x₀ = -5,  y₀ = -4

Therefore:

y - (-4) =  -³/₅(x - (-5))

y + 4 = -³/₅(x + 5)      ←  the point-slope form of the equation

y + 4 = -³/₅x - 3              {subtract 4 from both sides}

y = -³/₅x - 7               ←  the slope-intercept form of the equation

³/₅x + y = - 7                     {multiply both sides by 5}

3x + 5y = - 35               ←  standard form of the equation

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft