Question: Graph the equation $y = 4x - 2$.
Blue line rising left to right, passing through the red points $(0, -2)$ at center-left and $(2, 2)$ near center; position_hint \in \{center\}.
The slope is 4 and the y-intercept is $(0, -2)$.
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The slope of the line is |
This is not an integer.
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The y-intercept of the line is $(0,-2)$ (Enter as a point.)
1. **State the problem:** We need to graph the linear equation $$y = 4x - 2$$ and identify its slope and y-intercept.
2. **Recall the slope-intercept form:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept.
3. **Identify slope and y-intercept:** From $$y = 4x - 2$$, the slope $$m = 4$$ and the y-intercept $$b = -2$$.
4. **Plot the y-intercept:** The y-intercept is the point where the line crosses the y-axis, at $$(0, -2)$$.
5. **Use the slope to find another point:** The slope $$4$$ means rise over run is $$\frac{4}{1}$$. Starting from $$(0, -2)$$, move up 4 units and right 1 unit to reach $$(1, 2)$$.
6. **Plot the second point:** Plot the point $$(1, 2)$$.
7. **Draw the line:** Connect the points $$(0, -2)$$ and $$(1, 2)$$ with a straight line extending in both directions.
8. **Verify with another point:** Using the equation, for $$x=2$$, $$y=4(2)-2=8-2=6$$, so point $$(2, 6)$$ lies on the line.
**Final answer:** The line has slope $$4$$ and y-intercept $$(0, -2)$$, passing through points $$(0, -2)$$, $$(1, 2)$$, and $$(2, 6)$$.