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The equation of the line is \( y = 10x - 3 \).
Solución
To find the equation of a line given the slope and the \( y \)-intercept, we can use the slope-intercept form of a linear equation, which is given by:
\[
y = mx + b
\]
where:
- \( m \) is the slope,
- \( b \) is the \( y \)-intercept.
From the problem, we have:
- Slope \( m = 10 \)
- \( y \)-intercept \( b = -3 \)
Now, we can substitute these values into the slope-intercept form:
\[
y = 10x - 3
\]
This is the equation of the line with a slope of 10 and a \( y \)-intercept of -3.
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Simplifique esta solución The Deep Dive
Did you know that the equation of a line can be easily expressed in the slope-intercept form, which is \( y = mx + b \)? In your case, with a slope of 10 and a \( y \)-intercept of -3, the equation becomes \( y = 10x - 3 \). This means for every unit increase in \( x \), the \( y \)-value goes up by 10! A fun way to visualize this line is by plotting it on a graph. Start at the \( y \)-intercept (-3) on the \( y \)-axis and from there, use the slope: rise 10 units up for every 1 unit you move to the right. This will help you see how steeply the line climbs—it's quite dramatic!
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