Graph the linear equation 2x + y − 1 = 0, find its x-intercept and y-intercept.

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ScanSolve AI Tutor · Accepted Answer

Here's the solution for Exercise 6.6, Question 1: The equation given is 2x + y − 1 = 0. Step 1: Rearrange the equation to solve for y. y = −2x + 1 Step 2: Create a table of values by choosing several x-values and calculating the corresponding y-values. x — y = −2x + 1 — (x, y)−1 — y = −2(−1) + 1 = 2 + 1 = 3 — (−1, 3); 0 — y = −2(0) + 1 = 0 + 1 = 1 — (0, 1); 1 — y = −2(1) + 1 = −2 + 1 = −1 — (1, −1); 2 — y = −2(2) + 1 = −4 + 1 = −3 — (2, −3) Step 3: Determine the x-intercept. The x-intercept is the point where the graph crosses the x-axis, meaning y = 0. 0 = −2x + 1; 2x = 1; x = 1/2 The x-intercept is (1/2, 0). Step 4: Determine the y-intercept. The y-intercept is the point where the graph crosses the y-axis, meaning x = 0. y = −2(0) + 1; y = 1 The y-intercept is (0, 1). To draw the graph, plot the points from the table of values, including the x-intercept and y-intercept, and then draw a straight line through them.

$x$	$y = -2x + 1$	$(x, y)$
-1	$y = -2(-1) + 1 = 2 + 1 = 3$	$(-1, 3)$
0	$y = -2(0) + 1 = 0 + 1 = 1$	$(0, 1)$
1	$y = -2(1) + 1 = -2 + 1 = -1$	$(1, -1)$
2	$y = -2(2) + 1 = -4 + 1 = -3$	$(2, -3)$

Graph the linear equation 2x + y − 1 = 0, find its x-intercept and y-intercept.

Answer

Step-by-step solution

Rearrange the equation to solve for $y$ .

Create a table of values by choosing several $x$ -values and calculating the corresponding $y$ -values.

Determine the x-intercept.

Determine the y-intercept.

Try one yourself

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More Mathematics Questions

Key points of y = −2x + 1
Point	x	y
y-intercept	0	1
x-intercept	0.5	0

Graph the linear equation 2x + y − 1 = 0, find its x-intercept and y-intercept.

Answer

Step-by-step solution

Rearrange the equation to solve for yyy.

Create a table of values by choosing several xxx-values and calculating the corresponding yyy-values.

Determine the x-intercept.

Determine the y-intercept.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Rearrange the equation to solve for $y$ .

Create a table of values by choosing several $x$ -values and calculating the corresponding $y$ -values.