Linear Equations Notes Practice Things to remember An

Linear Equations Notes & Practice

Things to remember An equation = a statement in algebra that says 2 expressions are equivalent Variables in linear equations only have power of 1 You must balance each side at all times (What you do to one side MUST be done to the other side!).

How to approach them ● If equation has fractions, but the answers don’t, try clearing the fractions in the equation by multiplying by the least common denominator ● The presence of fractions in the answer choices likely means you’ll need to rely on techniques for combining and simplifying fractions to get to the right answer ● Seeing decimals in the answer choices likely indicates that using your calculator will save time on test day.

Working with Linear Graphs - - When a linear equation in written in slope-intercept form (y= mx+b), the variable m gives the slope of the line & b represents the point at which the line intersects the y-axis In a real-world scenario, slope represents a unit rate and the y-intercept represents a starting amount The rate of change (slope) for a linear relationship is constant (DOES NOT VARY) Slope is given by the formula m = y 2 - y 1/ x 2 - x 1 (X 1, y 1) & (x 2, y 2) are coordinates of points on the line *Remember RISE OVER RUN

Working with Linear Graphs cont. - A line with a positive slope runs up and to the right (“uphill”) A line with a negative slope runs down and to the right (“downhill”) A horizontal line has a slope of 0 (with NO rise to left or right!) A vertical line has an undefined slope Parallel lines have the same slope Perpendicular lines have negative reciprocal slopes (ex: 3 and -⅓) *To find a graph that matches a given equation (& vice versa), find the slope (m) of the line and its y-intercept (b).

SLOPE = RATE

x= independent variable y= dependent variable “Infinite # of solutions” = solve for the variable

Practice 1 3 y + 2(y-2) = -25 What value of y satisfies the equation above? A) -29/5 B) -21/5 C) 21/5 D)29/5

Practice 1 answer 3 y + 2(y-2) = -25 What value of y satisfies the equation above? A) -29/5 B) -21/5 C) 21/5 D)29/5

Reasoning Start by distributing the 2. Then collect like terms until you isolate y. 3 y + 2(y-2) = -25 3 y + 2 y - 4 = -25 5 y - 4 = -25 Y = -21/5

Line L has an undefined slope. Line M is perpendicular to line L. Which of the following could be the equation of line M? A) B) C) D) x=y y=7 x=-3 xy=4

Line L has an undefined slope. Line M is perpendicular to line L. Which of the following could be the equation of line M? A) B) C) D) x=y y=7 x=-3 xy=4 Reasoning: Undefined slope = VERTICAL line; therefore, parallel to y-axis! - A line that is perpendicular to a vertical line MUST be a horizontal line. Horizontal line slope = 0 - Its equation, therefore, will be of the form y=0 x+b - It can also be seen as y=b Remember that b is constant. The only equation that meets this criterion is choice B!

⅔ x+cy=2 If the slope of the equation above is 6, what is the value of c? A) B) C) D) -4 -1/9 ⅓ 4

⅔ x+cy=2 If the slope of the equation above is 6, what is the value of c? A) -4 B) -1/9 C) ⅓ D) 4 Explanation: Rewrite your formula in slopeintercept form! - You will need to subtract ⅔ x from both sides to do this and then divide both sides by c - Then, set the coefficient for x equal to the given slope (6) and solve for c. Since the coefficient is a fraction, write 6 as 6/1 and cross-multiply

A line in the xy-plane that passes through the coordinate points (3, -6) and (-7, -4) will never intersect a line that is represented by which of the following equations? A) B) C) D) x+5 y=6 x+y/2 = 7 y-2 x=-9 2 y-x = -8

A line in the xy-plane that passes through the coordinate points (3, -6) and (-7, -4) will never intersect a line that is represented by which of the following equations? A) B) C) D) x+5 y=6 x+y/2 = 7 y-2 x=-9 2 y-x = -8 Reasoning: Use m= y 2 -y 1 ------X 2 -x 1 to determine the slope of the line given in the question. You should come up with a slope of -⅕ - Next, identify the slope in the answer choices Remember: Parallel lines have = slope!

Let’s continue in your books! Open to page 40 and complete questions 1 -10 of the “extra practice problems. ” We will check them tomorrow!