Linear Equations and Graphs (TEKS A.2A)
What is the slope-intercept form of a linear equation?
The slope-intercept form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept.
What is a function?
A function is a relation where each input (x-value) has exactly one output (y-value).
What is point-slope form of a linear equation?
Point-slope form is y−y1=m(x−x1).
What is the inequality symbol for “less than”?
The symbol for "less than" is <.
If a taxi company charges a flat fee of $4 plus $2 per mile, write the linear function representing the total cost (C) for a ride of x miles.
C=4+2x
Find the slope of a line that passes through the points (2, 3) and (5, 9).
The slope is 2
Identify the domain and range of the relation { (1, 3), (2, 5), (3, 7), (4, 9) }
Domain: {1, 2, 3, 4}, Range: {3, 5, 7, 9}.
Convert y=−5x+3 to standard form.
In standard form: 5x+y=3
Graph the inequality y<2x+3 and describe the shaded region.
shade below the line
Solve for x in the equation 5x+7=22 and explain what this solution represents in a real-world context.
5x+7=22; subtract 7: 5x=15; divide by 5: x=3x. This solution could represent the number of items sold to meet a total price of $22, for example.
Write the equation of a line that has a slope of -2 and passes through the point (4, 1).
The equation is y−1=−2(x−4) or simplified, y=−2x+9.
Determine if the relation { (2, 3), (2, 5), (4, 7) } is a function and explain why or why not.
This is not a function because the x-value 2 has two different outputs, 3 and 5.
Write the equation of a line passing through (2, -1) and (6, 3) in point-slope form.
y+1=x−2.
Write an inequality that represents the graph of a line with a slope of 3, a y-intercept of -1, and shading below the line.
y<3x−1, with shading below the line.
If a line passes through the points representing the cost of apples, (1, 2) and (3, 6), what is the rate of change in the price per apple?
The rate of change, or slope, is 2 and it would mean about $2 per apple
Determine if the point (3, 7) lies on the line represented by the equation y=2x+1.
Substitute x=3: y=2(3)+1=7. Since y=7, the point (3, 7) lies on the line.
Describe the vertical line test and how it is used to determine if a graph represents a function.
he vertical line test states that if a vertical line passes through more than one point on a graph, the relation is not a function.
Given the line with equation 4x−2y=12, rewrite it in slope-intercept form.
In slope-intercept form: y=2x−6
Solve for x in the inequality 4x−7>9
4x−7>9; adding 7 gives 4x>16; dividing by 4 gives x>4x.
A cellphone plan costs $20 per month plus $0.10 per minute of usage. Write the equation to represent the total monthly cost (C) based on the number of minutes used (m), and find the cost if 250 minutes are used.
The cost is $45.
The slope is 34\frac{3}{4}43 and the y-intercept is -2 Convert the equation 3x−4y=8 to slope-intercept form and identify the slope and y-intercept.
The slope is 3/4 and the y-intercept is -2
This means that when the input is -2 ( the x) , the output is -4( the y).
Find the equation of a line that is parallel to y=(1/2)x-4 and passes through the point (2, 3).
y=(1/2)x +2
Determine whether the point (1, 2) satisfies the inequality y≥−x+5.
Substitute x=1: y=−1+5=4. Since 2≤4 , the point satisfies the inequality
In a race, Alex runs at a steady rate of 5 mph. Write the equation representing his distance over time, and determine how far he will have traveled after 2.5 hours.
The equation is d=5t. After 2.5 hours, d=5×2.5=12.5 miles.