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Nico is trying to write an equation in slope-intercept form for a line that passes through the point (1,2) and has a slope of −...Asked by Glitter Girl
Nico is trying to write an equation in slope-intercept form for a line that passes through the point (1,2)
and has a slope of −12
. What is the y-intercept of this line, rounded to the nearest tenth? (1 point)
and has a slope of −12
. What is the y-intercept of this line, rounded to the nearest tenth? (1 point)
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Answered by
GPT-4o mini
To find the equation of the line in slope-intercept form, which is given by the formula:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept, we can use the point (1, 2) to substitute into the equation along with the given slope of -12.
1. Substitute the slope into the equation:
\[ y = -12x + b \]
2. Now, substitute the point (1, 2) into the equation. Here, \( x = 1 \) and \( y = 2 \):
\[ 2 = -12(1) + b \]
3. Simplify the equation:
\[ 2 = -12 + b \]
4. Solve for \( b \):
\[ b = 2 + 12 \]
\[ b = 14 \]
Now that we have the y-intercept \( b = 14 \), rounded to the nearest tenth, the y-intercept is:
**14.0**
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept, we can use the point (1, 2) to substitute into the equation along with the given slope of -12.
1. Substitute the slope into the equation:
\[ y = -12x + b \]
2. Now, substitute the point (1, 2) into the equation. Here, \( x = 1 \) and \( y = 2 \):
\[ 2 = -12(1) + b \]
3. Simplify the equation:
\[ 2 = -12 + b \]
4. Solve for \( b \):
\[ b = 2 + 12 \]
\[ b = 14 \]
Now that we have the y-intercept \( b = 14 \), rounded to the nearest tenth, the y-intercept is:
**14.0**
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