Here is the graph of the linear equation y=2x-3:
[image]
The graph is a straight line that passes through the point (0, -3) and has a slope of 2.
Graph the linear equation. y=2x-3.
7 answers
write y-6x=5 in slope-intercept form
To write the equation y - 6x = 5 in slope-intercept form (y = mx + b), we need to solve for y and isolate it on one side of the equation.
Starting with the given equation: y - 6x = 5
Step 1: Add 6x to both sides of the equation to isolate the y-term:
y = 6x + 5
Therefore, the equation y - 6x = 5 can be written in slope-intercept form as y = 6x + 5.
Starting with the given equation: y - 6x = 5
Step 1: Add 6x to both sides of the equation to isolate the y-term:
y = 6x + 5
Therefore, the equation y - 6x = 5 can be written in slope-intercept form as y = 6x + 5.
Graph the equation x-y=6 using the form y=mx+b
To graph the equation x - y = 6 in slope-intercept form, we need to solve for y.
Starting with the given equation: x - y = 6
Step 1: Subtract x from both sides of the equation to isolate the y-term:
-y = -x + 6
Step 2: Divide all terms by -1 to get y by itself:
y = x - 6
Now the equation is in the form y = mx + b, where the slope (m) is 1 and the y-intercept (b) is -6.
To graph the equation, we can start by plotting the y-intercept at (0, -6), which is the point where the line crosses the y-axis.
Next, we can use the slope of 1 to find additional points on the line. For example, for every unit increase in x, we can increase y by 1. So, we can plot another point at (1, -5).
Finally, we can draw a straight line passing through the two plotted points. This line represents the graph of the equation x - y = 6.
The graph will be a diagonal line that starts at (0, -6) and has a positive slope of 1. As x increases, y also increases by 1.
Starting with the given equation: x - y = 6
Step 1: Subtract x from both sides of the equation to isolate the y-term:
-y = -x + 6
Step 2: Divide all terms by -1 to get y by itself:
y = x - 6
Now the equation is in the form y = mx + b, where the slope (m) is 1 and the y-intercept (b) is -6.
To graph the equation, we can start by plotting the y-intercept at (0, -6), which is the point where the line crosses the y-axis.
Next, we can use the slope of 1 to find additional points on the line. For example, for every unit increase in x, we can increase y by 1. So, we can plot another point at (1, -5).
Finally, we can draw a straight line passing through the two plotted points. This line represents the graph of the equation x - y = 6.
The graph will be a diagonal line that starts at (0, -6) and has a positive slope of 1. As x increases, y also increases by 1.
Describe what makes a proportion. Give an example of a proportion. (keep it to five sentences)
A proportion is a statement that two ratios or fractions are equal. In a proportion, the four terms are in a specific relationship: the product of the means (the terms in the middle) is equal to the product of the extremes (the first and last terms).
For example, a classic proportion is "3/4 = 6/8". In this example, the product of the means (4 * 6) is equal to the product of the extremes (3 * 8), which is 24.
The key characteristic of a proportion is that it maintains the same ratio or relationship between the terms, regardless of the actual values of the numbers involved. So, if the numbers in the proportion are multiplied or divided by the same non-zero value, the resulting equation is still a proportion.
Proportions are commonly used in various real-life scenarios, such as scaling recipes in cooking, calculating similar figures in geometry, or solving problems involving rates and proportions in mathematics or economics.
For example, a classic proportion is "3/4 = 6/8". In this example, the product of the means (4 * 6) is equal to the product of the extremes (3 * 8), which is 24.
The key characteristic of a proportion is that it maintains the same ratio or relationship between the terms, regardless of the actual values of the numbers involved. So, if the numbers in the proportion are multiplied or divided by the same non-zero value, the resulting equation is still a proportion.
Proportions are commonly used in various real-life scenarios, such as scaling recipes in cooking, calculating similar figures in geometry, or solving problems involving rates and proportions in mathematics or economics.