The equation of the line perpendicular to y = -4x + 2 and passing through the point (-8, 5) is y = (1/4)x + 7 in slope-intercept form.
To find the equation of a line perpendicular to the given line y = -4x + 2 and passing through the point (-8, 5), we first determine the slope of the given line. The given line is in the slope-intercept form y = mx + b, where m is the slope, and b is the y-intercept. In this case, the slope m is -4.
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. The negative reciprocal of -4 is 1/4. Therefore, the slope of the line we're looking for is 1/4.
Now, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope. Substituting the values (-8, 5) for (x1, y1) and 1/4 for m, we get:
y - 5 = (1/4)(x + 8)
To convert this equation to the slope-intercept form (y = mx + b), you can simplify and rearrange the terms. The final equation is:
y = (1/4)x + 7
Therefore, the slope-intercept form of the equation of the line passing through (-8, 5) and perpendicular to y = -4x + 2 is y = (1/4)x + 7.
Complete question:
Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the equation.
(-8,5): y = -4x + 2