Textbook Question
Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. horizontal, through (-7,4)
2. Graphs of Equations
Lines
1:42 minutesProblem 31
Textbook Question
Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. slope 0, y-intercept (0, 3/2)
Verified step by step guidance1
Identify the slope and y-intercept given in the problem. Here, the slope is 0, and the y-intercept is the point \( (0, \frac{3}{2}) \).
Recall that a slope of 0 means the line is horizontal. A horizontal line has the form \( y = b \), where \( b \) is the y-intercept.
Since the y-intercept is \( \frac{3}{2} \), the equation of the line in slope-intercept form is \( y = \frac{3}{2} \).
To write the equation in standard form, recall that standard form is \( Ax + By = C \), where \( A, B, \) and \( C \) are integers and \( A \geq 0 \).
Rewrite \( y = \frac{3}{2} \) as \( 0 \cdot x + y = \frac{3}{2} \), or simply \( y = \frac{3}{2} \), which is already in standard form with \( A=0, B=1, C=\frac{3}{2} \). If desired, multiply through by 2 to clear the fraction: \( 0 \cdot x + 2y = 3 \).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Slope of a Line
The slope measures the steepness of a line and is defined as the ratio of the vertical change to the horizontal change between two points. A slope of 0 means the line is horizontal, indicating no vertical change as you move along the line.
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The Slope of a Line
Y-Intercept
The y-intercept is the point where the line crosses the y-axis, represented as (0, b). It indicates the value of y when x is zero and is essential for writing the equation of a line.
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Forms of Linear Equations
Linear equations can be expressed in various forms, including standard form (Ax + By = C) and slope-intercept form (y = mx + b). The slope-intercept form explicitly shows the slope and y-intercept, while the standard form is a rearranged version often used for certain types of problems.
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