Question 3.4.3: Find the slope and y-intercept for the equation -2x + y = -4......
Find the slope and y-intercept for the equation -2x + y = -4. Then, use them to draw the graph.
Step 1:
To identify the slope and y-intercept from an equation, we need to write the equation in slope-intercept form, which is y = mx + b. In this form, the coefficient of x represents the slope (m) and the constant term represents the y-intercept (b).
Step 2:
In the given equation, -2x + y = -4, we can rearrange it to solve for y. To do so, we add 2x to both sides of the equation. This results in the equation y = 2x - 4, which is now in slope-intercept form.
Step 3:
From this equation, we can determine that the slope is 2 and the y-intercept is -4. The slope represents the rate of change of y with respect to x, meaning that for every increase of 1 in x, y will increase by 2. The y-intercept is the point where the graph of the equation crosses the y-axis, which in this case is at (0, -4).
Step 4:
To find another point on the graph, we can use the slope. We can let the rise be 2 and the run be 1, meaning that for every increase of 1 in x, y will increase by 2. Using this information, we can plot a second point on the graph.
Step 5:
Overall, the equation y = 2x - 4 represents a linear relationship with a slope of 2 and a y-intercept of -4. The graph of this equation will be a straight line passing through the point (0, -4) and with a slope of 2.
Final Answer
To identify the slope and y -intercept from the equation, the equation must be in the form y = mx + b (slope-intercept form). To write our equation in this form, we must solve the equation for y. To do so, we simply add 2x to each side of the equation.
-2x + y = -4 Original equation
y = 2x – 4 Add 2x to each side
The equation is now in slope-intercept form, so the slope must be 2 and the y -intercept – 4. The graph, therefore, crosses the y -axis at (0, -4) . Since the slope is 2, we can let the rise = 2 and the run = 1 and find a second point on the graph. The graph is shown in Figure 5.
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