Point-Slope Form of a Line Quiz

Study Notes

Point-Slope Form Overview

Point-slope form of a linear equation is expressed as ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is a point on the line and ( m ) is the slope.

Example Scenarios

The newspaper in Haventown had a circulation of 80,000 in 2000 and 50,000 in 2010. The point-slope equation for this scenario can be filled as ( y - 50,000 = -3,000(x - 10) ).
A linear function represented by the point-slope equation ( y + 1 = -3(x - 5) ) simplifies to ( f(x) = -3x + 14 ).

Student Steps in Equation Formation

Talia's steps to find the point-slope form were partially accurate. She correctly chose points and identified the slope; however, her slope calculation in Step 3 was incorrect.

Graphical Representations

The graph that corresponds with the equation ( y + 3 = 2(x + 3) ) includes points (-3, -3) and (0, 3).
Several linear functions may represent a graphed line, including ( f(x) = \frac{1}{2}x + 2 ), ( y - 3 = \frac{1}{2}(x - 2) ), and ( y - 1 = \frac{1}{2}(x + 2) ).

Slope Evaluations

The slope of the line given by the equation ( y - 4 = \frac{5}{2}(x - 2) ) is ( \frac{5}{2} ).
The slope from the equation ( y - 3 = -\frac{1}{2}(x - 2) ) is ( -\frac{1}{2} ).

Specific Line Equations

Harold's equation ( y = 3(x - 7) ) indicates he used the point (7, 0).
The equation representing a line passing through the point (4, ( \frac{1}{3} )) with a slope of ( \frac{3}{4} ) is ( y - \frac{1}{3} = \frac{3}{4}(x - 4) ).
For a line through (-9, -3) with a slope of -6, the equation is ( y + 3 = -6(x + 9) ).

Description

Test your understanding of the point-slope form of linear equations with these quiz flashcards. You'll answer questions involving real-world scenarios and converting point-slope equations into linear functions. Perfect for students looking to solidify their grasp on this essential algebra concept.