Algebra I: Write Linear Equations – Flashcards
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where m is the slope and (x1, y1) is a point on the line This is another format for straight line equations. Use when you know a point and the slope; it helps find the y-intercept
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point slope form
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the y-coordinate of the point where the line crosses the y-axis
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y - intercept
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1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17) 2 - Calculate the slope using the formula 3 - The y-intercept is 5 because the line crosses at (0,5) Write in slope intercept form: y = mx + b
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How to Write a Linear Function Ex: Write an equation for the linear function ƒ with the values ƒ(0) = 5 and ƒ(4) = 17.
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1 - Identify the slope m. You can use the slope formula if you know two points on the line. 2 - Find the y-intercept. You can substitute the slope and the coordinates (x, y) of a point on the line in y = mx + b. Then solve for b. 3 - Write an equation using y = mx + b
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How to Write an Equation of a Line in Slope-Intercept Form
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can be used to find the x- and y-intercepts. Ax + By = C A, B, C are integers (no fractions or decimals) A should be positive
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Standard Form
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the slope and the y-intercept
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What do you need to graph a line?
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plug the slope and a point into y = mx + b solve for b Write the equation
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Write the equation of a line that passes through the point with the given slope
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use the formula to find the slope plug the slope and a point into y = mx + b solve for b Write the equation
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Write the equation of a line in slope intercept form that passes through two points
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the statement formed by exchanging the hypothesis and conclusion of a conditional statement (the opposite)
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converse
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If two nonvertical lines in the same plane have the same slope, then they are parallel. If two nonvertical lines in the same plane are parallel, then they have the same slope.
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Parallel Lines
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1 - Identify the slope (in this case = 3) 2 - Use the slope and the point to solve for b in y = mx + b 3 - Write the equation using y = mx + b
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To Write an Equation of a Parallel Line: Write an equation of the line that passes through (-3, -5) and is parallel to the line y = 3x - 1
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If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular. If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.
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Perpendicular Lines
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write all equations in slope-intercept form ( y = mx + b) compare their m value: if the same, then parallel; if negative reciprocals, then perpendicular
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To determine whether lines are parallel or perpendicular
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is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.
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Scatter Plot
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y tends to increase, as x increases
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Positive Correlation
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y tends to decrease, as x increases
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Negative Correlation
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x and y have no apparent relationship
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Relatively No Correlation
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The line that most closely follows a trend in data is called the best-fitting line.
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Line of Best Fit
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the process of finding the best-fitting line to model a set of data; you can use technology to do this
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Linear Regression
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using a line or its equation to approximate a value between two known values
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Linear Interpolation
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1 - Make a scatter plot of the data 2 - Graph the best fitting line
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Interpolate Using an Equation
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using a line or its equation to approximate a value outside the range of known values
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Linear Extrapolation
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for the function ƒ, any number x such that ƒ(x) = 0
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Zeros of a Function
