Math

QuestionFind the xx-intercept and yy-intercept of the line 2x+4y=82x + 4y = -8 and use them to graph the line.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is x+4y=8x +4y = -8 . The xx-intercept is the point where the line crosses the xx-axis, at this point y=0y =0
3. The yy-intercept is the point where the line crosses the yy-axis, at this point x=0x =0

STEP 2

First, let's find the xx-intercept. We can do this by setting y=0y =0 in the given equation and solving for xx.
2x+4(0)=82x +4(0) = -8

STEP 3

implify the equation to find the xx-intercept.
2x=82x = -8

STEP 4

olve for xx by dividing both sides of the equation by2.
x=8/2x = -8 /2

STEP 5

Calculate the xx-intercept.
x=8/2=4x = -8 /2 = -4So, the xx-intercept is 4-4.

STEP 6

Now, let's find the yy-intercept. We can do this by setting x=0x =0 in the given equation and solving for yy.
2(0)+4y=82(0) +4y = -8

STEP 7

implify the equation to find the yy-intercept.
4y=4y = -

STEP 8

olve for yy by dividing both sides of the equation by4.
y=8/4y = -8 /4

STEP 9

Calculate the yy-intercept.
y=8/4=2y = -8 /4 = -2So, the yy-intercept is 2-2.

STEP 10

Now that we have the xx-intercept and the yy-intercept, we can graph the line. Plot the points (4,0)(-4,0) and (0,2)(0, -2) on the graph and draw a line through these points.
The xx-intercept is 4-4 and the yy-intercept is 2-2.

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