Schmidt Wright
03/30/2024 · Middle School
Find the point slope form of a line with Slope: -2 that passes through \( (4,3) \) \( (y-\square)=\square(x-\square) \) Write the line in slope intercept form below: \( y=\square \)
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Step-by-step Solution
To find the point-slope form of a line with a slope of -2 that passes through the point (4, 3), we can use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Here, \( m = -2 \), \( x_1 = 4 \), and \( y_1 = 3 \).
Substituting these values into the formula, we get:
\[
y - 3 = -2(x - 4)
\]
So, in point-slope form, the equation is:
\[
(y - 3) = -2(x - 4)
\]
Now, to write the line in slope-intercept form \( y = mx + b \), we can simplify the point-slope form:
1. Distribute the slope on the right side:
\[
y - 3 = -2x + 8
\]
2. Add 3 to both sides:
\[
y = -2x + 8 + 3
\]
\[
y = -2x + 11
\]
Thus, the slope-intercept form of the line is:
\[
y = -2x + 11
\]
To summarize:
- Point-slope form: \( (y - 3) = -2(x - 4) \)
- Slope-intercept form: \( y = -2x + 11 \)
Quick Answer
Point-slope form: \( (y - 3) = -2(x - 4) \)
Slope-intercept form: \( y = -2x + 11 \)
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