Question

Write an equation in slope-intercept form for a line that is parallel to the line y = -2x + 5 and passes through the point (4, -5).

Answer 1

To write the equation of a parallel line, use the slope and a point on the line. Substitute the values into the point-slope form, then simplify to slope-intercept form.

Step-by-step explanation:

To write an equation in slope-intercept form for a line that is parallel to the line y = -2x + 5 and passes through the point (4, -5), we need to determine the slope of the given line. Since the line is parallel, the slope will be the same. The slope-intercept form of a line is y = mx + b, where m represents the slope and b is the y-intercept. So, let's find the slope of the given line: y = -2x + 5.

1. Identify the slope of the given line: -2 (the coefficient of x).
2. Use the point-slope form of a line to write the equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.
3. Substitute the values of the point (4, -5) and the slope (-2) into the equation.
4. Simplify the equation to slope-intercept form (y = mx + b) by solving for y.

By following these steps, we find that the equation of the line parallel to y = -2x + 5 and passing through (4, -5) is y = -2x - 13.