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

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

Options:

Correct Answer: y = -3x + 11

Solution:

Using y = mx + b: 5 = -3(2) + b => 5 = -6 + b => b = 11. Thus, y = -3x + 11.

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

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

Step 1: Identify the slope (m) and the point (x, y) given in the problem. Here, the slope m = -3 and the point is (2, 5).
Step 2: Write the slope-intercept form of the equation, which is y = mx + b, where b is the y-intercept.
Step 3: Substitute the slope (m) into the equation. This gives us y = -3x + b.
Step 4: Substitute the x and y values from the point (2, 5) into the equation. This means we replace y with 5 and x with 2: 5 = -3(2) + b.
Step 5: Calculate -3(2) which equals -6. Now the equation looks like: 5 = -6 + b.
Step 6: To find b, add 6 to both sides of the equation: 5 + 6 = b, which simplifies to b = 11.
Step 7: Now we have both m and b. Substitute b back into the equation: y = -3x + 11.
Step 8: The final equation of the line in slope-intercept form is y = -3x + 11.

Slope-Intercept Form – Understanding the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
Point-Slope Calculation – Using a given point and slope to find the y-intercept by substituting values into the slope-intercept equation.