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

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

Options:

Correct Answer: 11

Solution:

Using the point-slope form: y - 5 = -3(x - 2). Solving for y gives y = -3x + 11, so the y-intercept is 11.

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

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

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

Slope-Intercept Form – Understanding how to derive the equation of a line using slope and a point.
Point-Slope Form – Using the point-slope form of a linear equation to find the y-intercept.