Answer:
y=-\frac{5}{3} x+\frac{10}{3} or what is the same: [tex]5x+3y=10[/tex]
Step-by-step explanation:
First we find the slope of the line that goes through the points (-4,10) and (-1,5) using the slope formula: [tex]slope=\frac{10-5}{-4-(-1)} =\frac{5}{-3} =-\frac{5}{3}[/tex]
Now we use this slope in the general form of the slope- y_intercept of a line:
[tex]y=-\frac{5}{3} x+b[/tex]
We can determine the parameter "b" by requesting the condition that the line has to go through the given points, and we can use one of them to solve for "b" (for example requesting that the point (-1,5) is on the line:
[tex]y=-\frac{5}{3} x+b\\5=-\frac{5}{3} (-1)+b\\5=\frac{5}{3}+b\\5-\frac{5}{3}=b\\b=\frac{10}{3}[/tex]
Therefore, the equation of the line in slope y_intercept form is:
[tex]y=-\frac{5}{3} x+\frac{10}{3}[/tex]
Notice that this equation can also be written in an equivalent form by multiplying both sides of the equal sign by "3", which allows us to write it without denominators:
[tex]y=-\frac{5}{3} x+\frac{10}{3}\\3*y=(-\frac{5}{3} x+\frac{10}{3})*3\\3y=-5x+10\\5x+3y=10[/tex]
The required equation is 3y + 5x = 10
The standard form of an equation is expressed as:
y = mx + b where:
m is the slope
b is the y-intercept
Given the coordinate points (–4, 10) and (–1, 5)
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{5-10}{-1+4}\\m=\frac{-5}{3}\\[/tex]
Get the y-intercept
[tex]5 = -5/3(-1) + b\\5 = 5/3 + b\\b = 5-5/3\\b= 10/3\\[/tex]
Get the required equation:
[tex]y=\frac{-5}{3}x+\frac{10}{3}[/tex]
Rewrite in the form Ax+By = C
[tex]y=\frac{-5}{3}x+\frac{10}{3}\\y=\frac{-5x+10}{3}\\3y=-5x+10\\3y+5x = 10[/tex]
Hence the required equation is 3y + 5x = 10
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