What is the slope of the line shown in the graph?
- \(1\)
- \(2\)
- \(\frac{1}{2}\)
- \(4\)
Testinar Grade 8 math
Slope and the Equations of a Line
Learn to reason about and solve Grade 8 problems involving Slope and the Equations of a Line.
CH03-03
Equations, Inequalities, and Systems
- Name
- Date
- Score
- ____ / 8
-
-
What is the equation of the line shown?
- \(y=-\frac{1}{2}x+\frac{9}{2}\)
- \(y=2x+2\)
- \(y=-2x+6\)
- \(y=\frac{1}{2}x+3\)
-
The table shows the relationship between \(x\) and \(y\) on a line. What is the slope?
- \(2\)
- \(11\)
- \(\frac{1}{3}\)
- \(3\)
-
Which equation represents the relationship shown in the table?
- \(y=-2x+3\)
- \(y=2x+3\)
- \(y=-x+3\)
- \(y=3x-2\)
-
What is the equation of the line shown?
- \(y=-\frac{1}{2}x-2\)
- \(y=-2x-2\)
- \(y=\frac{1}{2}x-2\)
- \(y=2x-2\)
-
Which ordered pair is a solution to the equation of the line shown?
- \((1,3)\)
- \((2,1)\)
- \((4,1)\)
- \((3,2)\)
-
What is the \(y\)-intercept of the line shown?
- \(1\)
- \(4\)
- \(3\)
- \(2\)
-
What is the slope represented by the table?
- \(1\)
- \(2\)
- \(3\)
- \(6\)
Answer key and explanations
-
A. \(1\)
Using points \((0,1)\) and \((4,5)\): slope \(= \frac{5-1}{4-0} = \frac{4}{4} = 1\).
-
A. \(y=-\frac{1}{2}x+\frac{9}{2}\)
Using \((1,4)\) and \((5,2)\): slope \(= \frac{2-4}{5-1} = -\frac{1}{2}\). Substituting: \(4 = -\frac{1}{2}(1) + b\) gives \(b = \frac{9}{2}\).
-
D. \(3\)
The slope is the rate of change: \(\frac{\Delta y}{\Delta x} = \frac{3}{1} = 3\) (each increase of 1 in \(x\) gives 3 more in \(y\)).
-
A. \(y=-2x+3\)
Slope \(= \frac{3-7}{0-(-2)} = \frac{-4}{2} = -2\). When \(x=0\), \(y=3\), so \(b=3\). Thus \(y=-2x+3\).
-
A. \(y=-\frac{1}{2}x-2\)
The \(y\)-intercept is \(-2\). Using \((4,-4)\): slope \(= \frac{-4-(-2)}{4-0} = \frac{-2}{4} = -\frac{1}{2}\).
-
A. \((1,3)\)
The line passes through \((0,4)\) and \((3,1)\), so slope \(= -1\) and \(y=-x+4\). For \(x=1\), the equation gives \(y=3\), so \((1,3)\) is on the line.
-
D. \(2\)
The \(y\)-intercept is where the line crosses the \(y\)-axis, which occurs at \((0,2)\).
-
C. \(3\)
As \(x\) increases by 1, \(y\) increases by 3. Slope \(= \frac{\Delta y}{\Delta x} = \frac{3}{1} = 3\).
