Section 2.4 – More about Linear Equations

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Presentation transcript:

Section 2.4 – More about Linear Equations The slopes of two lines in the same plane indicate how the lines are related. Given the slope and y-intercept, you can write the equation of a line in slope-intercept form. You can also write the equation of a line in point-slope form.

Section 2.4 – More about Linear Equations Here is why it works: By substituting the general point (x, y) for (x2, y2) in the slope formula, you can rewrite the slope formula in point-slope form.

Section 2.4 – More about Linear Equations Problem 1: A line passes through (-5, 2) with a slope of 3/5. What is an equation of the line? Problem 1b: A line passes through (7, -1) with a slope of -3. What is an equation of the line?

Section 2.4 – More about Linear Equations Problem 2: A line passes through (-3, 2) and (5, 8). What is an equation of the line in point slope form? In slope-intercept form? Problem 2b: A line passes through (-5, 0) and (0, 7). What is an equation of the line in point slope form? In slope-intercept form?

Section 2.4 – More about Linear Equations Another form of the equation of a line is standard form, in which the sum of x and y terms are set equal to the constant. When possible, you write the coefficients of x and y and the constant term as integers.

Section 2.4 – More about Linear Equations Problem 3: What is an equation of the line y = 3/4x – 5 in standard form? Use integer coefficients. Problem 3b: What is an equation of the line y = 9.1x + 3.6 in standard form. Use integer coefficients.

Section 2.4 – More about Linear Equations You can graph an equation in standard form quickly by determining the x- and y- intercepts and then drawing the line through them.

Section 2.4 – More about Linear Equations Problem 4: What are the intercepts of 3x + 5y = 15? Problem 3b: What are the intercepts of 2x – 4y = 8?

Section 2.4 – More about Linear Equations Problem 5: The number of times a cricket chirps per minute depends on the temperature. The number of chirps in 2 seconds for two temperatures are shown. What graph models the situation? What is an equation of the line in standard form? If the temperature is 70 degrees, how many times would you expect a cricket to chirp in one minute?

Section 2.4 – More about Linear Equations Problem 5: The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows that the paper will last about 80 days. What graph models the situation? What is an equation of the line in standard form? If the temperature is 70 degrees, how many times would you expect a cricket to chirp in one minute?

Section 2.4 – More about Linear Equations

Section 2.4 – More about Linear Equations Problem 6: What is the equation of each line in slope-intercept form? The line parallel to y = 6x – 2 through (1, -3) The line perpendicular to y = -4x + 2/3 through (8, 5) The line parallel to 4x + 2y = 7 through (4, -2) The line perpendicular to y = 2/3x – 1 through (0, 6)

Section 2.4 – More about Linear Equations Lesson Check

Section 2.4 – More about Linear Equations Lesson Check