Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations?

x + 2y = 8
2x + 4y = 12

A) The slopes are different, and the y-intercepts are different.
B) The slopes are different, and the y-intercepts are the same.
C) The slopes are the same, and the y-intercepts are different.
D) The slopes are the same, and the y-intercepts are the same.

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notyet notyet · Answer 1 · 2020-04-26T18:23:23+02:00

The answer is C because when written in y=Mx+b format they both have a slope of -1/2 but different y intercepts

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saimaparvezVT saimaparvezVT · Answer 2 · 2022-08-04T15:26:31+02:00

The answer would be option(C) The slopes are the same, and the y-intercepts are different.

The slope of equation x + 2y = 8 is -1/2 and y-intercept is 4.

The slope of equation 2x + 4y = 12 is -1/2 and y-intercept is 3.

Slope of line is defined as the angle of line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The slope intercept form of a linear equation is

y = mx + c

where, m is slope and c is y-intercept.

The given system of equations is

x + 2y = 8

2x + 4y = 12

The slope intercept form of given equations are

x + 2y = 8

2y = 8 - x

Divided by 2 both the sides

y = 4 - x/2

Here, the slope of equation is -1/2 and y-intercept is 4.

2x + 4y = 12

4y = 12 - 2x

Divided by 4 both the sides

y = 3 - x/2

Here, the slope of equation is -1/2 and y-intercept is 3.

Learn more about Slope of Line here:

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