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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A line passes through point (-2, 5) and has a slope of . Points A(x, 3) and B(-2, y) lie on the line. The value of x is , and the value of y is .

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MissPhiladelphia
For the answer to the question above asking what is A line passes through a point (-2, 5) and has a slope of. Points A(x, 3) and B(-2, y) lie on the line. The value of x is, and the value of y is?

y = mx + b
slope (m) = 2/3
(-2,5)...x = -2 and y = 5
now we sub and find b, the y int
5 = 2/3(-2) + b
5 = -4/3 + b
5 + 4/3 = b
15/3 + 4/3 = b
19/3 = b

so ur equation of the line is : y = 2/3x + 19/3
-2/3x + y = 19/3
-2x + 3y = 19
2x - 3y = -19

(x,3).....so sub in 3 for y
2x - 3(3) = -19
2x - 9 = -19
2x = -19 + 9
2x = - 10
x = -5......so point A is (-5,3)

(-2,y).....x = -2
2(-2) - 3y = -19
-4 - 3y = -19
-3y = -19 + 4
-3y = -15
y = 5......so the otherpoint is (-2,5)

The value of x is -5 and y is 5.

Given

A line passes through the point (-2, 5) and has a slope of 2/3.

Points A(x, 3) and B(-2, y) lie on the line.

What is the slope of the line?

The slope of a line gives the measure of its steepness and direction.

The formula is used to find the slope of the line is;

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line.

A line passes through the point (-2, 5) and has a slope of 2/3.

Then,

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}\\\\\dfrac{2}{3} = \dfrac{y-5}{x-(-2)}\\\\\dfrac{2}{3} = \dfrac{y-5}{x+2}\\\\ 2(x+2) = 3(y-5)\\\\2x+4=3y-15\\\\2x-3y=-15-4\\\\2x-3y=-19[/tex]

Point A(x,3) and B(-2,y) lie on the line. It means it satisfies the equation of the line.

Here, y = 3 substitute in the equation.

[tex]\rm 2x-3y=-19\\\\2x-3(3)=-19\\\\2x-9=-99\\\\2x=-19+9\\\\ 2x=-10 \\\\x=\dfrac{-10}{2}\\\\ x=-5[/tex]

Substitute the value of x = -2 in the equation

[tex]\rm 2x-3y=-19\\\\2(-2)-3y=-19\\\\-4-3y=-19\\\\-3y=-19+4\\\\-3y=-15\\\\y = \dfrac{-15}{-3} \\\\ y = 5[/tex]

Hence, the required value of x is -5 and y is 5.

To know more about Slope click the link given below.

https://brainly.com/question/2514839