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Math  /  Geometry

QuestionFind the intercepts. Then graph by using the intercepts, if possible. 2y−x=62 y-x=6
Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. □\square xtbook Ask my instructor Search

Studdy Solution

STEP 1

1. The equation given is 2y−x=62y - x = 6.
2. To find the intercepts, we need to determine the points where the line crosses the x-axis and y-axis.
3. For the x-intercept, set y=0y = 0 and solve for xx.
4. For the y-intercept, set x=0x = 0 and solve for yy.
5. Use the intercepts to plot the line on a graph.

STEP 2

1. Find the x-intercept.
2. Find the y-intercept.
3. Use the intercepts to graph the line.

STEP 3

To find the x-intercept, set y=0y = 0 in the equation 2y−x=62y - x = 6:
2(0)−x=62(0) - x = 6

STEP 4

Simplify the equation to solve for xx:
−x=6-x = 6
x=−6x = -6
So, the x-intercept is (−6,0)(-6, 0).

STEP 5

To find the y-intercept, set x=0x = 0 in the equation 2y−x=62y - x = 6:
2y−0=62y - 0 = 6

STEP 6

Simplify the equation to solve for yy:
2y=62y = 6
y=3y = 3
So, the y-intercept is (0,3)(0, 3).

STEP 7

Now, we have the intercepts (−6,0)(-6, 0) and (0,3)(0, 3). Plot these points on a graph.

STEP 8

Draw a line through the points (−6,0)(-6, 0) and (0,3)(0, 3).
Solution: The intercepts of the line 2y−x=62y - x = 6 are (−6,0)(-6, 0) and (0,3)(0, 3). Using these intercepts, the line can be graphed.

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