Question

question 5
sketch a graph of the linear equation:
y = -3x + 2
graph grid
clear all draw:
submit question

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-3x + 2\), the y - intercept \(b = 2\), so the line crosses the y - axis at \((0,2)\). The slope \(m=-3=\frac{-3}{1}\), which means for every 1 unit we move to the right (increase in \(x\) by 1), we move down 3 units (decrease in \(y\) by 3).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,2)\) and mark it.

Step3: Use the slope to find another point

From \((0,2)\), move 1 unit to the right (to \(x = 1\)) and 3 units down (since the slope is - 3). So we get the point \((1,2 - 3)=(1,-1)\). We can also move 1 unit to the left (to \(x=- 1\)) and 3 units up (because moving left is a decrease in \(x\) by 1, and using the slope formula \(y - y_1=m(x - x_1)\), when \(x=-1\), \(y-2=-3(-1 - 0)\), \(y - 2 = 3\), \(y=5\)), so the point \((-1,5)\) is also on the line.

Step4: Draw the line

Connect the points (e.g., \((0,2)\), \((1,-1)\), \((-1,5)\)) with a straight line.

To sketch the graph of \(y=-3x + 2\):

1. Plot the y - intercept at \((0,2)\).
2. Use the slope \(-3\) to find additional points (e.g., \((1,-1)\) or \((-1,5)\)).
3. Draw a straight line through these points.

(Note: Since the problem is about drawing the graph, the key steps are identifying the intercept and slope to plot points and draw the line. If you were to describe the graph, it is a straight line with a negative slope of 3, crossing the y - axis at (0,2) and sloping downward from left to right.)

Answer:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-3x + 2\), the y - intercept \(b = 2\), so the line crosses the y - axis at \((0,2)\). The slope \(m=-3=\frac{-3}{1}\), which means for every 1 unit we move to the right (increase in \(x\) by 1), we move down 3 units (decrease in \(y\) by 3).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,2)\) and mark it.

Step3: Use the slope to find another point

From \((0,2)\), move 1 unit to the right (to \(x = 1\)) and 3 units down (since the slope is - 3). So we get the point \((1,2 - 3)=(1,-1)\). We can also move 1 unit to the left (to \(x=- 1\)) and 3 units up (because moving left is a decrease in \(x\) by 1, and using the slope formula \(y - y_1=m(x - x_1)\), when \(x=-1\), \(y-2=-3(-1 - 0)\), \(y - 2 = 3\), \(y=5\)), so the point \((-1,5)\) is also on the line.

Step4: Draw the line

Connect the points (e.g., \((0,2)\), \((1,-1)\), \((-1,5)\)) with a straight line.

To sketch the graph of \(y=-3x + 2\):

1. Plot the y - intercept at \((0,2)\).
2. Use the slope \(-3\) to find additional points (e.g., \((1,-1)\) or \((-1,5)\)).
3. Draw a straight line through these points.

(Note: Since the problem is about drawing the graph, the key steps are identifying the intercept and slope to plot points and draw the line. If you were to describe the graph, it is a straight line with a negative slope of 3, crossing the y - axis at (0,2) and sloping downward from left to right.)