Final answer:
To find the equation of a line perpendicular to another line, we determine the negative reciprocal of the slope. Using the given point and slope, we can write the equation in point-slope form and then convert it to slope-intercept form.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line. The given line is in the form 5x=5-y, which can be rewritten as y=-(5x+5). Therefore, the slope of the given line is -5. The negative reciprocal of -5 is 1/5.
So, the slope of the line we are looking for is 1/5. We can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (-1.5, 3.4) and the slope 1/5, the equation of the line is y - 3.4 = 1/5(x - (-1.5)). Simplifying this equation, we get y - 3.4 = 1/5(x + 1.5).
To write the equation in slope-intercept form, we need to solve for y. Distributing 1/5 on the right side and adding 3.4 to both sides, we get y = 1/5x + 1.87.
Therefore, the equation of the line that passes through (-1.5, 3.4) and is perpendicular to the line 5x=5-y is y = 1/5x + 1.87.