Mathematics, 02.01.2022 04:30 kimlyn58p0wyn0

Find the equation of the line in the picture
(Use exact numbers)

y= ? x+ ?

Find the equation of the line in the picture
(Use exact numbers)
y= ? x+ ?

Answers: 3

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Answer from: maddo36

y = -3x + 7

Step-by-step explanation:

In order to determine the linear equation in slope-intercept form, y = mx + b, we must first determine its slope, and y-intercept.

Slope:

The slope (also referred to as the rate of change) is the measure of the steepness of a line. We can solve for the slope of the line using the following slope formula:

$\displaystyle\mathsf{\textbf{Slope\:(m)} =\:\frac{y_2 - y_1}{x_2 - x_1}}$

We must choose two points from the graph.

Let (x₁, y₁) = (1, 4)

(x₂, y₂) = (0, 7)

Substitute these values into the slope formula:

$\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}$

$\displaystyle\mathsf{Slope\:(m) =\:\frac{7-4}{0-1}\:=\frac{3}{-1}\:=\:-3}$

Hence, the slope of the line is -3.

Y-intercept:

Next, we must determine the y-intercept of the graph. The y-intercept is the point on the graph where it crosses the y-axis, with its coordinates occurring at point (0, b). The value of "b" is the y-intercept that we use in the slope-intercept form.

Observing the given graph, it shows that the line crosses the y-axis at point (0, 7). Therefore, the y-intercept, b = 7.

Linear Equation:

Now that we have our slope, m = -3, and y-intercept, b = 7, we can write the following linear equation in slope-intercept form:

y = -3x + 7

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

Answer from: Quest

exactly you go it

step-by-step explanation:

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Find the equation of the line in the picture
(Use exact numbers)

y= ? x+ ?
...