If a line has a slope of -2 and passes through the point (3, 5), what is its y-i

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Question: If a line has a slope of -2 and passes through the point (3, 5), what is its y-intercept?

Options:

Correct Answer: 3

Solution:

Using the point-slope form: y - y1 = m(x - x1) => y - 5 = -2(x - 3). Setting x = 0 gives y = 1.

If a line has a slope of -2 and passes through the point (3, 5), what is its y-intercept?

If a line has a slope of -2 and passes through the point (3, 5), what is its y-intercept?

Step 1: Identify the slope (m) and the point (x1, y1). Here, m = -2 and the point is (3, 5).
Step 2: Use the point-slope form of the equation of a line: y - y1 = m(x - x1).
Step 3: Substitute the values into the equation: y - 5 = -2(x - 3).
Step 4: Simplify the equation: y - 5 = -2x + 6.
Step 5: Add 5 to both sides to solve for y: y = -2x + 6 + 5.
Step 6: Combine the constants: y = -2x + 11.
Step 7: Identify the y-intercept, which is the constant term when x = 0. Here, the y-intercept is 11.

Point-Slope Form – The point-slope form of a linear equation is used to find the equation of a line given a point and the slope.
Finding the y-Intercept – The y-intercept is found by setting x to 0 in the equation of the line.