Graphing linear equations worksheet answerss
The phrase “graphing linear equations worksheet answerss” is interpreted as a request for a complete set of answers to a typical worksheet on graphing linear equations. A representative worksheet (8 problems) is included below, followed by the worksheet answers: slope, \(y\)-intercept, \(x\)-intercept, and two points that determine the line.
How to graph a linear equation (standard method)
- Rewrite the equation in slope-intercept form \(y=mx+b\) when possible.
- Read the slope \(m\) and the \(y\)-intercept \(b\) (point \((0,b)\)).
- Find a second point using either:
- the slope (rise/run from \((0,b)\)), or
- the \(x\)-intercept by setting \(y=0\).
- Plot the two points and draw the unique straight line through them.
Worksheet (problems)
| # | Linear equation to graph | Requested output |
|---|---|---|
| 1 | \(y=2x+1\) | Slope, intercepts, two points |
| 2 | \(y=-3x+6\) | Slope, intercepts, two points |
| 3 | \(2x+3y=12\) | Convert to \(y=mx+b\), then slope, intercepts, two points |
| 4 | \(4x-y=8\) | Convert to \(y=mx+b\), then slope, intercepts, two points |
| 5 | \(y-2=\frac{1}{2}(x+4)\) | Convert to \(y=mx+b\), then slope, intercepts, two points |
| 6 | \(y=\frac{3}{4}x-3\) | Slope, intercepts, two points |
| 7 | \(x+2y=-2\) | Convert to \(y=mx+b\), then slope, intercepts, two points |
| 8 | Line through points \((-2,5)\) and \((4,-1)\) | Equation, slope, intercepts, two points |
Worked example (one problem shown step-by-step)
Problem 3: \(2x+3y=12\). Solve for \(y\) to obtain slope-intercept form:
\[ 2x+3y=12 \quad\Rightarrow\quad 3y=12-2x \quad\Rightarrow\quad y=\frac{12-2x}{3} = -\frac{2}{3}x+4. \]
Slope \(m=-\frac{2}{3}\) and \(y\)-intercept \(b=4\), so one point is \((0,4)\). The \(x\)-intercept is found by setting \(y=0\): \(2x=12\Rightarrow x=6\), giving \((6,0)\). These two points determine the graph.
Worksheet answers (slope, intercepts, points)
| # | Slope-intercept form \(y=mx+b\) | Slope \(m\) | \(y\)-intercept | \(x\)-intercept | Two points to plot |
|---|---|---|---|---|---|
| 1 | \(y=2x+1\) | \(2\) | \((0,1)\) | \(\left(-\frac{1}{2},0\right)\) | \((0,1)\), \((1,3)\) |
| 2 | \(y=-3x+6\) | \(-3\) | \((0,6)\) | \((2,0)\) | \((0,6)\), \((2,0)\) |
| 3 | \(y=-\frac{2}{3}x+4\) | \(-\frac{2}{3}\) | \((0,4)\) | \((6,0)\) | \((0,4)\), \((6,0)\) |
| 4 | \(y=4x-8\) | \(4\) | \((0,-8)\) | \((2,0)\) | \((0,-8)\), \((2,0)\) |
| 5 | \(y=\frac{1}{2}x+4\) | \(\frac{1}{2}\) | \((0,4)\) | \((-8,0)\) | \((0,4)\), \((-2,3)\) |
| 6 | \(y=\frac{3}{4}x-3\) | \(\frac{3}{4}\) | \((0,-3)\) | \((4,0)\) | \((0,-3)\), \((4,0)\) |
| 7 | \(y=-\frac{1}{2}x-1\) | \(-\frac{1}{2}\) | \((0,-1)\) | \((-2,0)\) | \((0,-1)\), \((-2,0)\) |
| 8 | \(y=-x+3\) | \(-1\) | \((0,3)\) | \((3,0)\) | \((-2,5)\), \((4,-1)\) |
Visualization: three worksheet lines on one coordinate plane
Final answer
Graphing linear equations worksheet answerss consist of the slope \(m\), intercepts, and two reliable plot points for each equation; converting to \(y=mx+b\) produces the values shown in the worksheet answers table above.