Pregunta
Find the slope-intercept equation of the line that has the given characteristics. Slope 8 and y-intercept \( (0,6) \) The slope-intercept equation is (Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer.)
Ask by Wheeler Davison. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
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The slope-intercept equation is \( y = 8x + 6 \).
Solución
To find the slope-intercept equation of a line, we use the slope-intercept form of a linear equation, which is given by:
\[
y = mx + b
\]
where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept.
From the problem, we know:
- The slope \( m = 8 \),
- The y-intercept \( b = 6 \).
Now, we can substitute these values into the slope-intercept form:
\[
y = 8x + 6
\]
Thus, the slope-intercept equation of the line is:
\[
\boxed{y = 8x + 6}
\]
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Simplifique esta solución Beyond the Answer
To find the slope-intercept equation, we use the formula \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Here, the slope \(m\) is 8, and the y-intercept \(b\) is 6. Plugging these values into the formula gives us: \(y = 8x + 6\). Yay, we’ve got our equation, and it’s all set to go! If you ever wonder about the beauty of a straight line, just remember, it’s all about consistency! The slope tells us how much y changes for a change in x. In this case, for every increase of 1 in x, y increases by 8. Understanding this can really help you in geometry and physics, where lines and slopes often play a big role!
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