Final answer:
To find the equation of the line that is perpendicular to y = -5x + 19 and passing through the point (3, 3), we take the negative reciprocal of the slope of the given line (-5) to get 1/5. By substituting the coordinates of the given point into the equation, we can find the value of 'b' and write the equation in slope-intercept form as y = (1/5)x + 2.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = -5x + 19 and passing through the point (3, 3), we first need to determine the slope of the given line. The slope of a line in slope-intercept form (y = mx + b) is represented by the 'm' term. In the given line, the slope is -5.
To find the slope of a line perpendicular to another line, we take the negative reciprocal of the slope of the given line. The negative reciprocal of -5 is 1/5.
Therefore, the equation of the line that passes through (3, 3) and is perpendicular to y = -5x + 19 can be written as y = (1/5)x + b. We can find the value of 'b' by substituting the coordinates of the given point into the equation. Plugging in (3, 3), we get 3 = (1/5)(3) + b. Solving this equation gives us b = 2.
So, the equation of the line is y = (1/5)x + 2, in slope-intercept form.