How do you find the y-intercept from point-slope form?

To find the y-intercept from the point-slope form of a linear equation, you can follow these steps:

• Understand point-slope form: The point-slope form is given as y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.
• Rearrange the equation: To find the y-intercept, you need to express the equation in the slope-intercept form y = mx + b, where b is the y-intercept. Start by isolating y:

y = m(x - x_1) + y_1

• Expand the equation: Multiply through by the slope m to get:

y = mx - mx_1 + y_1

• Identify the y-intercept: The y-intercept b is the constant term in this equation. Hence, you can express it as:

b = -mx_1 + y_1

• Conclusion: You can find the y-intercept by substituting the values of the slope m and the coordinates of the point (x_1, y_1) into the equation for b.

For example, if you have a slope of 2 and a point (3, 5), the calculation for the y-intercept would be:

b = -2(3) + 5 = -6 + 5 = -1

Thus, the y-intercept is -1.