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Question
Math
Posted about 1 month ago

Use the given conditions to write an equation for the line in slope-intercept form.
Passing through (5,1)(-5,1) and perpendicular to the line whose equation is y=5/3x+1y=5 / 3 x+1
Write an equation for the line in slope-intercept form.
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Answer from Sia
Posted about 1 month ago
Solution by Steps
step 1
To find the slope of the line perpendicular to y=53x+1y = \frac{5}{3}x + 1, we first identify the slope of the given line, which is 53\frac{5}{3}
step 2
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the perpendicular line is 35-\frac{3}{5}
step 3
Now, we need to write the equation of a line with slope 35-\frac{3}{5} passing through the point (5,1)(-5, 1). We use the point-slope form of the equation: yy1=m(xx1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is the point (5,1)(-5, 1) and mm is the slope 35-\frac{3}{5}
step 4
Substituting the values, we get: y1=35(x+5)y - 1 = -\frac{3}{5}(x + 5)
step 5
Simplifying the equation: y1=35x3y - 1 = -\frac{3}{5}x - 3
step 6
Adding 1 to both sides to get the equation in slope-intercept form: y=35x2y = -\frac{3}{5}x - 2
Answer
y=35x2y = -\frac{3}{5}x - 2
Key Concept
Slope of perpendicular lines
Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.

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