Equation of a linear function

Question

What is the equation of a line that whose slope is -3 and passes through the point (1, -5)

Answer 1

To find the equation of a line with a given slope and a point through which it passes, we can use the point-slope form of a linear equation, which is:

y−y1=m(x−x1)y - y_1 = m(x - x_1)Where:

1. mm is the slope of the line.
2. (x1,y1)(x_1, y_1) is the point through which the line passes.

Given:

1. The slope m=−3m = -3
2. The point (x1,y1)=(1,−5)(x_1, y_1) = (1, -5)

Step 1: Substitute the given values into the point-slope form:

y−(−5)=−3(x−1)y - (-5) = -3(x - 1)Simplifying:

y+5=−3(x−1)y + 5 = -3(x - 1)Step 2: Distribute the slope on the right-hand side:

y+5=−3x+3y + 5 = -3x + 3Step 3: Solve for yy to put the equation in slope-intercept form (y=mx+by = mx + b):

Subtract 5 from both sides:

y=−3x+3−5y = -3x + 3 - 5 y=−3x−2y = -3x - 2Final Answer:

The equation of the line is:

y=−3x−2\boxed{y = -3x - 2}

Answer 2

1. Start with the formula:

y = m(x - h) + k where :

• m is the slope.

• (h, k) is a point on the line.

*Remember: h is opposite the x-value, k is keep the y-value the same!

2. Identify the slope: The slope m is -3.

3. Identify the point: The point is (1, -5).

4. Substitute values:

• Replace m with -3.

• Replace h with - 1 (OPPOSITE THE X!).

• Replace k with -5 (KEEP THE Y ! )

5. Final Answer:

The linear function in point-slope form is:

y = -3(x - 1) - 5

*Note : To go from Point - slope to Slope intercept just distribute and combine like terms!

Slope intercept form : y = -3x - 2