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3 years ago

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

ystem of equations?
(Graph)
4x + 2y = −2
x − 3y = 24

The slopes are different, and the y-intercepts are different.
The slopes are different, and the y-intercepts are the same.
The slopes are the same, and the y-intercepts are different.
The slopes are the same, and the y-intercepts are the same.

2 answers:

MakcuM [25]3 years ago

5 0

Answer:

The slopes are different, and the y-intercepts are different

Step-by-step explanation:

The lines on the graph are not parallel, so the slopes are different.

The lines on the graph intersect the y-axis in different places, so the y-intercepts are different.

Ilya [14]3 years ago

4 0

Answer:

<h2><em>The slopes are different, and the y-intercepts are different.</em></h2>

Step-by-step explanation:

<h3>From the graph:</h3>

Parallel lines have the same slope.

The lines are not parallel, therefore have the different slopes.

y-intercepts are different (look at the picture)

-1 and -8.

Answer:

<h3><em>The slopes are different, and the y-intercepts are different.</em></h3><h3 /><h3>From the system of equations:</h3>

The slope-ntercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

We have the equations of a lines in the standard form (Ax + By = C).

Convert ot the slope-intercept form:

$4x+2y=-2$ <em>subtract 4x from both sides</em>

$2y=-4x-2$ <em>divide both sides by 2</em>

$y=-2x-1$

Therefore we have the slope <em>m = -2</em>, and the y-intercept <em>b = -1</em>.

$x-3y=24$ <em>subtract x from both sides</em>

$-3y=-x+24$ <em>divide both sides by (-3)</em>

$y=\dfrac{1}{3}x-8$

Therefore we have the slope <em>m = 1/3</em>, and the y-intercept <em>b = -8</em>.

<em>-2 ≠ 1/3 </em><em>and </em><em>-1 ≠ -8</em>

<h3><em>The slopes are different, and the y-intercepts are different.</em></h3><h3 />

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