Question

The point-slope form of a line with a slope of 1/4 and passing through the point (3, 0) is given as y-0=¼(x-3). What is the equation in slope-intercept form?

a) y=¼x-3
b) y=¼x-¾
c) y=¾x-¼
d) y=¼x-1/12

Answer 1

The equation in slope-intercept form is y = ¼x - ⅔, obtained by distributing the slope ¼ throughout the point-slope form and simplifying.

Step-by-step explanation:

The student is given the point-slope form of a line, which is y-0=¼(x-3) and is asked to convert it to slope-intercept form. In slope-intercept form, the equation is expressed as y = mx + b, where m stands for the slope, and b is the y-intercept. To convert the point-slope equation to slope-intercept form, we simply need to distribute the slope and simplify:

• y - 0 = ¼(x - 3)
• y = ¼x - ¼×3
• y = ¼x - ⅔

Therefore, the equation in slope-intercept form is y = ¼x - ⅔, which corresponds to option b) y=¼x-¾.