Question

How do you determine the slope-intercept form given one point and a slope? a) y = mx + b

b) y - y₁ = m(x - x₁)
c) y = x + b
d) y = mx - b

Answer 1

The slope-intercept form y = mx + b can be determined by substituting the given slope (m) and point (x1, y1) into the equation and solving for the y-intercept (b). This results in the full equation of the line. Hence, Option B is correct.

Step-by-step explanation:

To determine the slope-intercept form of a linear equation given one point and a slope, you start with the standard form of the slope-intercept equation, y = mx + b, where m is the slope and b is the y-intercept. Imagine you are given a point (x1, y1) and a slope m. You would plug in the slope for m and the coordinates of the point for x and y, then solve for b, the y-intercept. This allows you to express the equation of the line in slope-intercept form.

Here's a step-by-step process:

1. Start with the slope-intercept form: y = mx + b.
2. Substitute the slope (m) and the coordinates of the given point (x1, y1) into the equation.
3. Solve for b by using the expression y1 = mx1 + b.
4. Once you find the value of b, write down the full slope-intercept equation using the slope and the calculated y-intercept.

For example, if a line passes through the point (2, 3) and has a slope of 4, substitute the values into the equation: 3 = 4(2) + b, and solve for b to get b = -5. The complete slope-intercept form of the equation would then be y = 4x - 5.