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To determine the equation of a line from a table of values, first identify two points from the table, typically in the form (x₁, y₁) and (x₂, y₂). Calculate the slope (m) using the formula ( m = \frac{y₂ - y₁}{x₂ - x₁} ). Then, use the point-slope form ( y - y₁ = m(x - x₁) ) to find the equation of the line. If necessary, rearrange it into slope-intercept form ( y = mx + b ).
What else can I help you with?
What is the equation of the line from the table of values?
To determine the equation of a line from a table of values, first identify two points from the table, typically represented as (x₁, y₁) and (x₂, y₂). Calculate the slope (m) using the formula ( m = \frac{y₂ - y₁}{x₂ - x₁} ). Then, use the point-slope form of the equation ( y - y₁ = m(x - x₁) ) to derive the line's equation, or convert it to slope-intercept form ( y = mx + b ) if needed.
How is a linear function represented in a table?
A linear function can be represented in a table by listing pairs of input (x) and output (y) values that satisfy the linear equation, typically in the form y = mx + b, where m is the slope and b is the y-intercept. Each row in the table corresponds to a specific x-value, with its corresponding y-value calculated using the linear equation. As the x-values increase or decrease, the y-values will change linearly, reflecting a constant rate of change. This results in a straight-line relationship when graphed.
Is point (2 1) on the line represented by the equation x 2y 5?
Without an equality sign and not knowing the plus or minus values of 2y and 5 it can't be considered to be a straight line equation.
Is point (2 1) on the line represented by the equation x plus 2y 5?
Without an equality sign and not knowing the plus or minus values of 2y and 5 it can't be considered to be a straight line equation.
How can you compare a linear function represented in a table to one represented as a graph?
To compare a linear function in a table to one represented as a graph, you can examine key characteristics such as the slope and y-intercept. In the table, the slope can be determined by calculating the change in y-values divided by the change in x-values between two points. On the graph, the slope is visually represented by the steepness of the line, while the y-intercept is the point where the line crosses the y-axis. Both representations should reflect the same linear relationship if they describe the same function.
What is the equation of the line from the table of values?
To determine the equation of a line from a table of values, first identify two points from the table, typically represented as (x₁, y₁) and (x₂, y₂). Calculate the slope (m) using the formula ( m = \frac{y₂ - y₁}{x₂ - x₁} ). Then, use the point-slope form of the equation ( y - y₁ = m(x - x₁) ) to derive the line's equation, or convert it to slope-intercept form ( y = mx + b ) if needed.
How is a linear function represented in a table?
A linear function can be represented in a table by listing pairs of input (x) and output (y) values that satisfy the linear equation, typically in the form y = mx + b, where m is the slope and b is the y-intercept. Each row in the table corresponds to a specific x-value, with its corresponding y-value calculated using the linear equation. As the x-values increase or decrease, the y-values will change linearly, reflecting a constant rate of change. This results in a straight-line relationship when graphed.
Is point (2 1) on the line represented by the equation x 2y 5?
Without an equality sign and not knowing the plus or minus values of 2y and 5 it can't be considered to be a straight line equation.
Is point (1 2) on the line represented by the equation x 2y 5?
Without an equality sign and not knowing the plus or minus values of 2y and 5 it can't be considered to be a straight line equation.
Is point (2 1) on the line represented by the equation x plus 2y 5?
Without an equality sign and not knowing the plus or minus values of 2y and 5 it can't be considered to be a straight line equation.
How can you compare a linear function represented in a table to one represented as a graph?
To compare a linear function in a table to one represented as a graph, you can examine key characteristics such as the slope and y-intercept. In the table, the slope can be determined by calculating the change in y-values divided by the change in x-values between two points. On the graph, the slope is visually represented by the steepness of the line, while the y-intercept is the point where the line crosses the y-axis. Both representations should reflect the same linear relationship if they describe the same function.
What does solving the equation for a line tell us?
A line is represented by an equation. Each solution of the equation is a point on the line, and each point on the line is a solution to the equation. So the line is just the graph of the solution set of the equation.
What is the y-intercept of the line represented by the equation below y-2x-1?
-1
How do you recognize a proportional relationship in a table?
A proportional relationship in a table can be recognized when the ratio of the values in one column to the corresponding values in another column remains constant. This means that if you divide the values of one column by the values of the other, the result will be the same for all pairs of values. Additionally, if you plot the points represented by the table on a graph, they will lie on a straight line that passes through the origin (0,0).
Where did the word linear equation came from?
It is an equation which, if plotted will be represented by a straight line (hence linear).
How can you determine if a relationship is linear from a table a graph or an equation?
To determine if a relationship is linear from a table, check if the differences in the y-values (output) corresponding to equal differences in the x-values (input) are constant. For a graph, a linear relationship will appear as a straight line. In an equation, if the equation can be expressed in the form (y = mx + b), where (m) and (b) are constants, it indicates a linear relationship.
What does a zero slope look like?
in a graph, a line with a zero slope is the one that is parallel to the x-axis. It is represented by an equation of the form y = a constant, independent of x values.
